Определение. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
--- класс групп. Подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGSgFmagi2FAwAjDxIjjNCzKmGEhUPF/KP4n65ZTjE+coMty3GSLGRhk33jk1RsSI47XMLArjKMWEiuO07D6+lhJYwaGu8bRDT7EiOM1rCHa2IeBwfhubHm5FHKAw8Xr6yWJNgwpoP+h4f+4vIjVsI6ONB4PGYY96DFFyItYDavP8zCUZZC9iR5bEC9ij0WchoGjXsZjT1pHBw8x4jgNKy+PlQJ5Bd2LuMRxGgZJjEiBDQ1odHF8BjIMvVKDHAwAHJvDHhGGI9oAAAAASUVORK5CYII=)
группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADlSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAaUh9p7AvU9J9B1mM3suKGaGMfkLisW04xXpfAFBpHN/hgsyDHTbYYXQ7VBXkehrIMDG9AzsblzTw34xSPvHpDnIZAwsD4bmx9vSS+AEYPZDijoyONx0OGYQ+DjMce5HCAi4PCCI6N7yBbhPBKfaykMQPDXVxewRWoJBkCClCcXsUME9k36AEH9xIOC1BjB+KaO2Aby8ulYIFYneViBIo1XNGONRoxUioIoyW8IZqL6WYIAGDsxF7fD3CIAAAAAElFTkSuQmCC)
называется
-инъектором, если для каждой субнормальной подгруппы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGSgFDPQ1BAgYIRhbOIEDclxky0GKvwPxf9k3XKK0cT/Mch67E7r6ODB65KGaGMfkAbj6AYfmFh9noehLIPxydj6ekmivAO2VcZjD8g2kPOjjBkWIttO0JCOjjQeDxmGPSBvlJfHShkzMNxBdhFRhkCcLXvTzc24loHB+A6684kyBBYeDAyybzzy6g3JimKw/0081oK8BHTJXZJdUl8fKwkMg7ugMICFDSyAiTYE4hWE7TBD8RmEwikvT+MF22wctRBZvDrLxUiWgeEN2KDycl6chkAD8x8cQ9MEhjhSCqZPBqS7IQDwRJYylElZywAAAABJRU5ErkJggg==)
группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADlSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAaUh9p7AvU9J9B1mM3suKGaGMfkLisW04xXpfAFBpHN/hgsyDHTbYYXQ7VBXkehrIMDG9AzsblzTw34xSPvHpDnIZAwsD4bmx9vSS+AEYPZDijoyONx0OGYQ+DjMce5HCAi4PCCI6N7yBbhPBKfaykMQPDXVxewRWoJBkCClCcXsUME9k36AEH9xIOC1BjB+KaO2Aby8ulYIFYneViBIo1XNGONRoxUioIoyW8IZqL6WYIAGDsxF7fD3CIAAAAAElFTkSuQmCC)
пересечение
![](data:image/png;base64,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)
является
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
-максимальной подгруппой в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADhSURBVDjLY2hsbGSgFDPQ1BAgYIRhbOIEDclxky0GKvwPw7JuOcVo4v8YZDz2pHV08OB1SUO0sQ9Ig3F0gw9MrD7Pw1CWwehUbH29JFHeAdsKtQ3k/ChjhoXIthM0pKMjjcdDhmEPyBv19bGSxgwMd5FdRJQhEGfL3nRzM65lYDC+i+58ogyBhQcDg+wbj7x6Q7KiGOx/E4+1IC+R5RLkMICFDa4AxWkIxCsI22GG4jMIhVNensYLttk4aiGyeHWWi5EsA8MbsEHl5bw4DYEG5j84htqMIQ7EsBRMnwxId0MAI9CWRCZBTJkAAAAASUVORK5CYII=)
.
Определение. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
--- класс групп. Подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGSgFmagi2FAwAjDxIjjNCzKmGEhUPF/KP4n65ZTjE+coMty3GSLGRhk33jk1RsSI47XMLArjKMWEiuO07D6+lhJYwaGu8bRDT7EiOM1rCHa2IeBwfhubHm5FHKAw8Xr6yWJNgwpoP+h4f+4vIjVsI6ONB4PGYY96DFFyItYDavP8zCUZZC9iR5bEC9ij0WchoGjXsZjT1pHBw8x4jgNKy+PlQJ5Bd2LuMRxGgZJjEiBDQ1odHF8BjIMvVKDHAwAHJvDHhGGI9oAAAAASUVORK5CYII=)
группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADlSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAaUh9p7AvU9J9B1mM3suKGaGMfkLisW04xXpfAFBpHN/hgsyDHTbYYXQ7VBXkehrIMDG9AzsblzTw34xSPvHpDnIZAwsD4bmx9vSS+AEYPZDijoyONx0OGYQ+DjMce5HCAi4PCCI6N7yBbhPBKfaykMQPDXVxewRWoJBkCClCcXsUME9k36AEH9xIOC1BjB+KaO2Aby8ulYIFYneViBIo1XNGONRoxUioIoyW8IZqL6WYIAGDsxF7fD3CIAAAAAElFTkSuQmCC)
называется
-биектором, если
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADEAAAATCAYAAAA5+OUhAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGcSURBVEjH7VY7bgIxEJ30cAAQ5g5o+pTGBWkjAaIK2gptQ+EqMtttkwvQcQ64CBLcIGeAYGcXmYl/ibYhAmkKZtcz8+a9Z4CiKODe4+4B/H8Ql89THSn5xgYK1PfO5Co0QdhcXjxXcWJ8sQzlmwqlZh0EOOja0BO7rCxb9bOyzFqCwbbuDTjZRJlYcLYEYJ8iV4OUfJOxmuLI12OC7IPmvYXM1i20sXxMGr+RX85xzhjsaR/DVH+4thnygqhoPeJ0NUrJ+7d5od2KlHNGNmL69n0ejzOlOtf+uRggz+dJxr4WkLJrb1KN8YUW9rLIxNap6QiL9aD1wmzfaYZcEosZ+0TiHBtCeyZk+Nhze1AzR2VwvQSO/J1KyQnCbKwHO9ooRUo+zdL6wz6uXWzSQTUrDNheg/JJyQnCPph6Y9jvpFy7mg3XMvQSOM9f6UI1+z4pOUGYK5Tc0aF8ynCpYNVYPPuW10c/wzdfpJx1qZlC+SZBSJm1jZSkbLtkHOpNfsQsE1cGpvmYaf8C4vY6xgP1S0hKj3+xDxAPED/jCxMiMZ9LWAvrAAAAAElFTkSuQmCC)
является
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
-максимальной подгруппой в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAATCAYAAAByUDbMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADlSURBVDjLY2hsbGSgFmYYoYbV18dKGjMw3GVgYPjPIOOxJ62jgwcm19GRxuMhw7AHLAfCxlELiXJZQ7SxDwOD7BuPvHpDdLkoY9lebOI4DctzM06RlWW4iW472OVy7rOQXYzXMLB3PKKTIa4zvhtbXy8JNyzPw9DYLS+F6AiAaYCFn6xbTjGyi7F5EadhyBqijBkWwiIC5GI3Y7dabF7Eahi6BpArZRlkb4IMx+dFnEnDzS0vDCM5ACMCnxexGxbpYYeuAZZM5IyxxyJWw3CFCbaIwGsYxHZoykZLDoRicaSXGpRgACTFEUtAnt/KAAAAAElFTkSuQmCC)
, а
![](data:image/png;base64,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)
является
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
-максимальной в
![](data:image/png;base64,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)
для каждой нормальной подгруппы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAATCAYAAAByUDbMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADlSURBVDjLY2hsbGSgFmYYoYbV18dKGjMw3GVgYPjPIOOxJ62jgwcm19GRxuMhw7AHLAfCxlELiXJZQ7SxDwOD7BuPvHpDdLkoY9lebOI4DctzM06RlWW4iW472OVy7rOQXYzXMLB3PKKTIa4zvhtbXy8JNyzPw9DYLS+F6AiAaYCFn6xbTjGyi7F5EadhyBqijBkWwiIC5GI3Y7dabF7Eahi6BpArZRlkb4IMx+dFnEnDzS0vDCM5ACMCnxexGxbpYYeuAZZM5IyxxyJWw3CFCbaIwGsYxHZoykZLDoRicaSXGpRgACTFEUtAnt/KAAAAAElFTkSuQmCC)
.
Ясно, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
-биектор одновременно является
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
-проектором и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADeSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTgPLyNF6IvzH9DI9atFSKNdBwRRnUK/+QXcdA9dxIdwMAiiSEOwjol3cAAAAASUVORK5CYII=)
-инъектором группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADeSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAa0hBt7APU9J9BxmMPsmKYuKxbTjFel8AUGkc3+GCzIMdNthhdDkVBfZ6HoSwDwxuQs3F5M8/NOMUjr94QpyGQMDC+G1tfL4kvgNEDGc7o6Ejj8ZBh2IMeDnBxUBjBsfEdZIsQXqmPlTRmYLiLyyu4ApUkQ0ABitOrmGEi+wY94OBewmEBauxAXHMHbGN5uRQsEKuzXIxAsYYr2rFGI0ZKBWG0AB+iuZhuhgAAaEvEYAlBwx8AAAAASUVORK5CYII=)
.
Пример Примерами
-биекторов служат силовские
-подгруппы групп для класса
всех
-групп. Пример В группе
силовская 2-подгруппа является
-биектором. Пример Группа
не является метанильпотентной, но
-проекторы и
-инъекторы совпадают между собой и являются нехолловыми подгруппами порядка 24. Для локальной формации
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
каждая конечная разрешимая группа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADlSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAaUh9p7AvU9J9B1mM3suKGaGMfkLisW04xXpfAFBpHN/hgsyDHTbYYXQ7VBXkehrIMDG9AzsblzTw34xSPvHpDnIZAwsD4bmx9vSS+AEYPZDijoyONx0OGYQ+DjMce5HCAi4PCCI6N7yBbhPBKfaykMQPDXVxewRWoJBkCClCcXsUME9k36AEH9xIOC1BjB+KaO2Aby8ulYIFYneViBIo1XNGONRoxUioIoyW8IZqL6WYIAGDsxF7fD3CIAAAAAElFTkSuQmCC)
обладает единственным классом мопряженных
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
-проекторов. Если
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
--- радикальный класс, т. e. класс Фиттинга, то каждая конечная разрешимая группа содержит единственный класс сопряженных
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
-инъекторов. Но наиболее употребительными в современной алгебре классы конечных групп являются одновременно и локальными формациями, и радикальными классами. Поэтому вполне естественно встает вопрос о существовании
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
-биекторов в конечных разрешимых группах для локальной радикальной формации
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
.
В настоящей работе показывается, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
-биекторы во всех разрешимых группах существуют только в том случае, когда
![](data:image/png;base64,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)
совпадает с классам
![](data:image/png;base64,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)
всех разрешимых
![](data:image/png;base64,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)
-групп. Кроме того устанавливается, что в метанильпотентных группах существование
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABPSURBVDjLY2hsbGQgFaNyGBgYcWGsmqKMGRYCJf8D8T9s2Di6wQe7JhmPPWkdHTxEO2+oaCov58UXckSHHnLIjYzQk/XYTZImslM5TTUBAJaGLnsotRyoAAAAAElFTkSuQmCC)
-биектора превращает его в
![](data:image/png;base64,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)
-холловскую подгруппу, и приведен пример, показывающий, что в разрешимых группах ступени нильпотентности
![](data:image/png;base64,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)
это свойство нарушается.
Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
--- класс групп. Через
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAVCAYAAADFEfeTAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAHhSURBVEjH7ZY/bsIwFMZfd3oAEGbrAYjVGyArQ+dKgNgqBoQiVQwZEDJsWXoIrlE4AScoEjlBOQM0tnnBGDt/EFSo6mBBHMf+vfe+9yUwm83gXsdtNgV4ECPr/q/C4YE88JsEYAt1f9mPooq5bsjIKFm7p93pSx7kVcDCsFfzwFv0OK+K62mXioP3hA1H+joEF/Oc96rymTCs3QxOgdANguHoUJgn8zHOR1G/4tdhCbQzP4Ulaz/gzdJwNu3o12n0BhjeowAbhFHlPMKeAnor2x45GYGdvqE6gHxjpCI7ZulsZaSMTeRvojPbOrmvltFMOLkp7XyI/wGjbwJmPGh5eoQqa2TlKonZAPlBnGcvV1NdSnmbt5tJiWI98oPWYls5cKQ6MyrgkEBsZjYfzn9+T1K2MiN3aeisKRJLCXj7SRxuK50OZ56RCWbrsKJwaCeYDZe9XAwnARxmmlXW1IiNoJS9kK2p09JlNSO3RWtriDDsPyqdWWzjAGEGXKohVGeSNWN04oKzWYmUAYGFaADXc6lFaVktbCV6itFGnBZQ0E7KvPqccML9pS4OUQi41mDsifmAsVeXvhrQ+LoEEN8irizDWUmIv0A9HN8SsMs0UXkI/cyylUueudsPzX+4Pwv3A9CMlLnT2dprAAAAAElFTkSuQmCC)
обозначается совокупность всех простых чисел
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADOSURBVDjLY2hsbGSgBDPQxAAgYARhXHy8BtTneRjKMjC8Bmr4bxzd4BNlzLAQyP7HwGB8N7a+XpIoF9TXx0oaMciekpVluAkypKMjjcdDhmGPrFtOMVEGNEQb+zDIGp2KzKtXBfFJNgDkbJDNqN6SvemRV29IOAzAzjfajexfcDgYRy0kPhBlPVamlZfzgkIeEojGd7AFIFYDctxkiyGhDsU4bMZqADiwZGVXYvMrUQZUZ7kYgZ3f0cFDsgGIBAPEMh57iDWEYXBmJroaAACuHYVs4rDX8wAAAABJRU5ErkJggg==)
, для которых в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
существует неединичная
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADOSURBVDjLY2hsbGSgBDPQxAAgYARhXHy8BtTneRjKMjC8Bmr4bxzd4BNlzLAQyP7HwGB8N7a+XpIoF9TXx0oaMciekpNjuAEypKMjjcdDhmGPrFtOMVEGNEQb+zDIGp2KzKtXBfFJNgDkbJDNqN6SvemRV29IOAzAzjfajexfcDgYRy0kPhBlPVamlZfzgkIeEojGd7AFIFYDctxkiyGhDsU4bMZqADiwZGVXYvMrUQZUZ7kYgZ3f0cFDsgGIBAPEsh67iTWEYXBmJroaAACxUYVtzIdP9wAAAABJRU5ErkJggg==)
-подгруппа, т. е.
![](data:image/png;base64,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)
. Множество
![](data:image/png;base64,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)
называется
характеристикой класса ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADeSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTgPLyNF6IvzH9DI9atFSKNdBwRRnUK/+QXcdA9dxIdwMAiiSEOwjol3cAAAAASUVORK5CYII=)
.
Для любого множества простых чисел
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAPCAYAAAA71pVKAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzNQXTMQMOLDODWXl6fxesgw7AEq+g/E/6AYwTaOXoBVc0dHGo+HrOxKj7x6w2hj4/rY+npJZDG8zq7Pi1SNzKtXra+PlTQ2jq6HiHkYysp6rEzr6OAhys95bsYpMJuijBkWGkc3+BAVYGBb5dxngWwCsY0YjHaDnE+U5hw32WKYTQ3Rxj4MxlELiYoqsGIZjz0w/4GcLOuWU1xeHisFCwOsmkEBI8cgdwM5VEGugESR8R1sTmcYXMmTLpoB8D87403OWBAAAAAASUVORK5CYII=)
через
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAYCAYAAAAVibZIAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADoSURBVEjH3dWxDoIwEAbgc+cBJOEegtzu2FTDbCINKxPpwmwKW1+D0XfgRUjkWZSiNaSbeINKckMT8vEH7g5o2xa4C34Tna4NG2ptGckEegAaC2Pi8KacoINE9qW10QoUbkB5x4siDgg4SG1SPnRKWQmsw7Qfo8YUMQGMpJqMDXXnOe0CYUH9GUVVs6GuGkWZbzE21Cd0aVlRo2XqWgwRBjb09T7dUHCizxa7hqjbE75YttTjI07pfYUPXIMqpfaKyCgtD/JkdixJ3XC4rtBCHIWgc7gr3gbnjkB50Y3eLgfkD34nX43eAR8R1xU8sMPfAAAAAElFTkSuQmCC)
обозначается класс всех нильпотентных
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAPCAYAAAA71pVKAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFzNQXTMQMOLDODWXl6fxesgw7AEq+g/E/6AYwTaOXoBVc0dHGo+HrOxKj7x6w2hj4/rY+npJZDG8zq7Pi1SNzKtXra+PlTQ2jq6HiHkYysp6rEzr6OAhys95bsYpMJuijBkWGkc3+BAVYGBb5dxngWwCsY0YjHaDnE+U5hw32WKYTQ3Rxj4MxlELiYoqsGIZjz0w/4GcLOuWU1xeHisFCwOsmkEBI8cgdwM5VEGugESR8R1sTmcYXMmTLpoB8D87403OWBAAAAAASUVORK5CYII=)
-групп.
Лемма Если
--- класс Шунка, то
. Доказательство. Пусть
![](data:image/png;base64,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)
. Ясно, что примитивная нилпотентная группа имеет простой порядок. Если
![](data:image/png;base64,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)
--- произвольная примитивная факторгруппа группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADeSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAa0hBt7APU9J9BxmMPsmKYuKxbTjFel8AUGkc3+GCzIMdNthhdDkVBfZ6HoSwDwxuQs3F5M8/NOMUjr94QpyGQMDC+G1tfL4kvgNEDGc7o6Ejj8ZBh2IMeDnBxUBjBsfEdZIsQXqmPlTRmYLiLyyu4ApUkQ0ABitOrmGEi+wY94OBewmEBauxAXHMHbGN5uRQsEKuzXIxAsYYr2rFGI0ZKBWG0AB+iuZhuhgAAaEvEYAlBwx8AAAAASUVORK5CYII=)
, то
![](data:image/png;base64,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)
имеет простой порядок
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADOSURBVDjLY2hsbGSgBDPQxAAgYARhXHy8BtTneRjKMjC8Bmr4bxzd4BNlzLAQyP7HwGB8N7a+XpIoF9TXx0oaMciekpVluAkypKMjjcdDhmGPrFtOMVEGNEQb+zDIGp2KzKtXBfFJNgDkbJDNqN6SvemRV29IOAzAzjfajexfcDgYRy0kPhBlPVamlZfzgkIeEojGd7AFIFYDctxkiyGhDsU4bMZqADiwZGVXYvMrUQZUZ7kYgZ3f0cFDsgGIBAPEMh57iDWEYXBmJroaAACuHYVs4rDX8wAAAABJRU5ErkJggg==)
. Так как
![](data:image/png;base64,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)
, то
![](data:image/png;base64,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)
. Из определения класса Шунка получаем, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACsAAAATCAYAAAAJdPQAAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAG5SURBVEjH7ZYxbsIwFIZfdzgAFe7WA4CvgNwM9AAQZasYEMrCkAG1hi1n6ARjzwBHIScgZyC1HTs4ruOEtFKFBNITYOP3fr/3vRdgs9nArdjNCP13sez1wM2131iscqbbXwmloTdAACfoe4dZHHfM/QVBSxbvjP31uFYsFzbFsOMHCsPTXRTNugSTd1uAa23t4zHzmyGyWOrrq/loyC6Smuv2W0/wqxCHvL0uSjo/m05+Yz6GLQBOgih65N/jeNbx+nAA7G9rmZVCMz39Znmq9tqgQ2nQwwBHXrVL+fExoLTnFCs5Sm23UhYS/OaFdGDbk+U7ldCpCGyLiwn5EO8VySh9yRllJTGcN8mWQMTA5hqTDZW5ECs+FKwY3SnWEexlpjJbtvhvRNNFUbfNBOFNK2Lnvgt+K8VKdhLFTtPOLZ0tlb85BqKiLEkhnTzr/LYWK8FPbIHF2aeXzzYImA3tSopljKB0NF8N9fXLOLFfJEcFfZnn6kzNU7Ohq3TYx4jkRjGnnLpGVp4RVnLtnIvZC6c/MSl08P5hfeB8KOQ3M9hr0OnqoVHHrN60VQkofGlZv//ruou9NbHffg1w6y0c8gQAAAAASUVORK5CYII=)
. Таким образом,
![](data:image/png;base64,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)
. Обратно, если
![](data:image/png;base64,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)
, то для любого простого делителя порядка
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADlSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAaUh9p7AvU9J9B1mM3suKGaGMfkLisW04xXpfAFBpHN/hgsyDHTbYYXQ7VBXkehrIMDG9AzsblzTw34xSPvHpDnIZAwsD4bmx9vSS+AEYPZDijoyONx0OGYQ+DjMce5HCAi4PCCI6N7yBbhPBKfaykMQPDXVxewRWoJBkCClCcXsUME9k36AEH9xIOC1BjB+KaO2Aby8ulYIFYneViBIo1XNGONRoxUioIoyW8IZqL6WYIAGDsxF7fD3CIAAAAAElFTkSuQmCC)
существует подгруппа индекса
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADOSURBVDjLY2hsbGSgBDPQxAAgYARhXHy8BtTneRjKMjC8Bmr4bxzd4BNlzLAQyP7HwGB8N7a+XpIoF9TXx0oaMciekpVluAkypKMjjcdDhmGPrFtOMVEGNEQb+zDIGp2KzKtXBfFJNgDkbJDNqN6SvemRV29IOAzAzjfajexfcDgYRy0kPhBlPVamlZfzgkIeEojGd7AFIFYDctxkiyGhDsU4bMZqADiwZGVXYvMrUQZUZ7kYgZ3f0cFDsgGIBAPEMh57iDWEYXBmJroaAACuHYVs4rDX8wAAAABJRU5ErkJggg==)
. Так как
![](data:image/png;base64,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)
, то
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAAVCAYAAAD2KuiaAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAKISURBVFjD7Vg7TgMxEB16OAAo3o4DZC1ugMwWSHRISZQOpUBoJUSxBYpMum24AB0lVyCcICcAKTkBOQPgz3rXcca7ziIKIMUoH3vtmTfvzUwCk8kE/rP9bucBdqTVrf8pAOyAeJp0CcASOsnLKM933b1XjNyI/Z90cHf6JwDIsuFBDPF0yPm++e5uQE9lkIRd3dh7DTidk7NcPZNlB78aAB0ondvBG+tTeBRrC7OW56PdpAMvQPuPFRjkLUl598cBMJq0ra2WzWfOh/tu5leyLdYpwNwErKlfAVKBEM+wM4IcCgmmoN272PdRGZ619eyqvaXTOgjyLrMmM+xS3HP3kjI2Vq+I7tWZBUi1AFiBqAKiKbbqIBoESaZYMWp0nPbv5fuU0QsZ8O3lcWyypbNPZj76YkXPB5aPBeCjlbw4iuBVgmB0hR0u1xhl41GW7bWVgLQBpbzHe11B54XJYKH9RROLSt3XJKqQysJlh5+WJJ71Un5oX4ABYA5epX64BEoAkqNrkfqZfQemZ8wUS0U7THnvUPmCUN346cbgPdBGqq6SqoOjk4dN6Y9m0HE8BADTCldZg7TGUACwqqsQRlAtnSfk6fjyNm4LgAoUGWiaJFAOQ45vum6RpZ2wYAmoQ0nyZDRd9Nl5cxaEo2Lg2LQGuBnEahHGvCwb7WndrwNUytICNbgIFtW00rEn8/52Fl4DdMUnb4zRsW9kxdqgZh1M5R2+50p/7PmgqQ0aOoe0ne+aTUnTAus60nd8wsZoFACVkYL+P/2jxq4rEgBZQ+T3KWPna5QW9I0gem0DgpkUfUxxCkdB3RZDzUYVX9LXusOWj3eQUYHQ59C2GvrMv/4zZAvAFoAtAPAFJQZ5azntJNgAAAAASUVORK5CYII=)
и
![](data:image/png;base64,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)
. Лемма доказана.
Следствие Если
--- локальная формация, то
. Доказательство. Достаточно вспомнить, что локальная формация является насыщенной, а значит и классом Шунка.
Лемма Пусть
--- класс Шунка и
--- конечная нильпотентная группа. Если
--- подгруппа из
, то
является
-проектором в
тогда и только тогда, когда
---
-холловская подгруппа. Доказательство. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADNSURBVDjLY2hsbGSgFmagi2FAwAjDxIjjNCzKmGEhUPF/KP4n65ZTjE+coMty3GSLGRhk33jk1RsSI47XMLArjKMWEiuO07D6+lhJYwaGu8bRDT7EiOM1rCHa2IeBwfhubHm5FHKA10ca+4LF6+sliTYMKaD/oeH/uLyI1bCOjjQeDxmGPegxRciLWA2rz/MwlGWQvYkeWxCvY49FnIaBo17GY09aRwcPMeI4DSsvj5UCeQXdi7jEcRoGSYxIgQ0NaHRxfAYyDL1SgxwMABbwwxxpzlc8AAAAAElFTkSuQmCC)
---
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTAIS/Mf0Mj1q0VIo10HBFGdQr/5Bdx0D13Eh3AwCyToRcoMjSRwAAAABJRU5ErkJggg==)
-проtктор в группе
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAaUh9p7AvWJOuxG1lxQ7SxD1D8v6xbTjFel8AUGkc3+GCzIMdNthhdDtUFeR6GsgwMb0DOxuXNPDfjFI+8ekOchkDCwPhubH29JK7AxRbIcEZHRxqPhwzDHgYZjz3I4QAWl2XYDQ3c/xBsfAfZIoRX6mMljRkY7uLyCq5AJckQUIBi8yqOMJF945JVbYQsDvcqDgtQYwfimjtgG8vLpWCBWJ3lYgSKNVzRjjUaMVIqloQ3RHMx3QwBAAeNws/qhxftAAAAAElFTkSuQmCC)
. Так как
![](data:image/png;base64,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)
, то по лемме подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADNSURBVDjLY2hsbGSgFmagi2FAwAjDxIjjNCzKmGEhUPF/KP4n65ZTjE+coMty3GSLGRhk33jk1RsSI47XMLArjKMWEiuO07D6+lhJYwaGu8bRDT7EiOM1rCHa2IeBwfhubHm5FHKA10ca+4LF6+sliTYMKaD/oeH/uLyI1bCOjjQeDxmGPegxRciLWA2rz/MwlGWQvYkeWxCvY49FnIaBo17GY09aRwcPMeI4DSsvj5UCeQXdi7jEcRoGSYxIgQ0NaHRxfAYyDL1SgxwMABbwwxxpzlc8AAAAAElFTkSuQmCC)
является
![](data:image/png;base64,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)
-подгруппой. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGSgFDPQ1BAgYIRhbOIEDclxky0GKvwPxf9k3XKK0cT/Mch67E7r6ODB65KGaGMfkAbj6AYfmFh9noehLIPxydj6ekmivAO2VcZjD8g2kPOjjBkWIttO0JCOjjQeDxmGPSBvlJfHShkzMNxBdhFRhkCcLXvTzc24loHB+A6684kyBBYeDAyybzzy6g3JimKw/0081oK8BHTJXZJdUl8fKwkMg7ugMICFDSyAiTYE4hWE7TBD8RmEwikvT+MF22wctRBZvDrLxUiWgeEN2KDycl6chkAD8x8cQ9MEhjhSCqZPBqS7IQDwRJYylElZywAAAABJRU5ErkJggg==)
---
![](data:image/png;base64,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)
-холловская в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADoSURBVDjLY2hsbGSgFDMMHUOAgBGGSTYEpCnKmGEhkP4Hx8ZRC8vL03jdjN1q0zo6ePAaUh9p7AvWJOuxG1lxQ7SxD1D8v6xbTjFel0AN+G8c3eCDzYIcN9lidDlUA/I8DGUZGN6AnI3Lm3luxikeefWGOA2BhIHx3dj6eklcgYstkOGMjo40Hg8Zhj0MMh57kMMBLC7LsBsauP8h2PgOskUIr9THShozMNzF5RVcgUqSIaAAxeZVHGEi+wY94OBexWEBauxAXHMHbGN5uRQsEKuzXIxAsYYr2rFGI0ZKxZLwhmguppshABR9wtg0ubzwAAAAAElFTkSuQmCC)
подгруппа. Ясно, что
![](data:image/png;base64,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)
. Nак как
![](data:image/png;base64,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)
, то
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADhSURBVDjLY2hsbGSgFDPQ1BAgYIRhbOIEDclxky0GKvwPw7JuOcVo4v8YZDz2pHV08OB1SUO0sQ9Ig3F0gw9MrD7Pw1CWwehUbH29JFHeAdsKtQ3k/ChjhoXIthM0pKMjjcdDhmEPyBv19bGSxgwMd5FdRJQhEGfL3nRzM65lYDC+i+58ogyBhQcDg+wbj7x6Q7KiGOx/E4+1IC+R5RLkMICFDa4AxWkIxCsI22GG4jMIhVNensYLttk4aiGyeHWWi5EsA8MbsEHl5bw4DYEG5j84htqMIQ7EsBRMnwxId0MAI9CWRCZBTJkAAAAASUVORK5CYII=)
---
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADeSURBVDjLY2hsbGSgBGMKMDAw4tWAJo8iWZ/nYSjLwPCGQcZjT1pHBw+65hw32WKgAf+Noxt8cLqgIdrYB6RI1i2nGJvh6OJYnRllzLCQgcH4bmx9vSSI39GRxuMhw7CHwThqIcEwANtWHytpzMBwF6YB4nSEgQQNQHaysZtbLZhG8jdRBiAHGrq/iTIA7m8Ghn+4nI/XAHBAAqMzrz5SFTk8iDIAFpUwf+OKWqwGwBMTmo2QqJV945FXb4jTgPLyNF6IvzH9DI9atFSKNdBwRRnUK/+QXcdA9dxIdwMAiiSEOwjol3cAAAAASUVORK5CYII=)
-подгруппа и
![](data:image/png;base64,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)
.