Оказалось, что группы, у которых все
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальные подгруппы нильпотентны, не обязательно разрешимы и полное описание групп с таким свойством в неразрешимом случае было получено Янком, а в разрешимом случае В.А. Белоноговым. Группы, у которых все
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAATCAYAAACk9eypAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC3SURBVDjLY2hsbGQgBTPQXwMQMMIwQQ3l5bFSxgwMd4CK/4GwcWS9L04N9fWxksYMxrti6+slQfwcN9liBgbjuzA+hoaGvDyJtI4OHmQDjBhkT3nk1RsS5enqLBcjWePoHqI8DVYs67Eyrbycl6CGPA/ZIpin8foBh8b/sm45xURp6OhI4/GQYdhDtAYQjjJmWGgc3eCDUwNyLEM87rkCOahR4yHa2AfhWSCW9diNrniAUivVNQAAMb1C2gUcn0kAAAAASUVORK5CYII=)
-максимальные подгруппы абелевы, были описаны Я.Г. Берковичем в работе. Эти результаты получили развитие в работе В.Н. Семенчука, который дал полное описание разрешимых групп, у которых все их
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальные подгруппы сверхразрешимы.
В последние годы получен ряд новых интересных результатов о
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvg5brLFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs5yMZKV9VyR1tHBQ7RGUFREGcv2IvuZKI2gEMXmRLwa6yONfWXdckpgiQDkZI/IejucGkGKQJpAcYeKje/C4harRmiE/8PAxtELaJvIaaoRAKfWUA2TmaRHAAAAAElFTkSuQmCC)
-максимальных подгруппах, связанных с изучением их способа вложения в основную группу. В этой связи, прежде всего , в которых на языке
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальных подгрупп получены описания ряда важных классов групп. Напомним, что подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADbSURBVDjLzZNBCoMwEEWney+gmEPI3EGysAeoIVtX4qIKWUZ3OYbew4t04Q16htqoGwkxTaEtDQyBR3jwZybQdR18quDrMn1OZrm4U8YQev3woWtebkKrq4u/jFmmpAYgd1rJxIc7ZTnCAJgPvvxQJiUPEWBC1mY+3ClrGWYAOHEhon2z5QXPK5cy9JatUbZGmzUfRbTKlCoCGsNI0rJ+J6JVJiuaECA3c1pbdPsUD2V69A3EdCyUCny4VbY0WAgeLVF0xGa/9TbulG3LuGs2st7Gza3/7Uf/C9kTlXm3FqepImkAAAAASUVORK5CYII=)
группы
![](data:image/png;base64,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)
обладает свойством покрытия-изолирования, если для любого главного фактора
![](data:image/png;base64,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)
группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD4SURBVDjLY2hsbGSgFDMMDUOAgBEdw8SJMgSkMMqYYSGQ/gfHxlELy8vTeN2M3WrTOjp48BpSH2nsC9Yk67EbWXFDtLEPSFzWLacYr0ugBvw3jm7wwWZBjptsMbocioLqLBcjWQaGNwzG0QtweTPPzTjFI6/eEKchkDAwvhtbXy9JTABjGNLRkcbjIcOwh0HGYw9yOIDFZRl2QwP3P4Q2voNsESIs6mMljRkY7oJiAJs3oIH6Hz1QSTIEFKDYvIoRJtHGDAsYGGTfuGRVGyGLw72KwwLU6IW45g7YxvJyKVggwmINV7RjjUaIi5BSKpaENwRzMV0NAQAYqL46wntofwAAAABJRU5ErkJggg==)
выполняется одно из двух условий
![](data:image/png;base64,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)
или
![](data:image/png;base64,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)
. В работе доказано, что группа
![](data:image/png;base64,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)
разрешима тогда и только тогда, когда в
![](data:image/png;base64,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)
имеется такая
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvg5brLFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs5yMZKV9VyR1tHBQ7RGUFREGcv2IvuZKI2gEMXmRLwa6yONfWXdckpgiQDkZI/IejucGkGKQJpAcYeKje/C4harRmiE/8PAxtELaJvIaaoRAKfWUA2TmaRHAAAAAElFTkSuQmCC)
-максимальная разрешимая подгруппа, которая обладает свойством покрытия-изолирования. Отметим также, что в работе, а также в работе изучалось строение групп, в зависимоси от
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальных подгрупп их силовских подгрупп.
Пусть
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
- подгруппы группы
![](data:image/png;base64,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)
. Тогда подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADHSURBVDjLY2hsbGSgBDMMLQOqs1yMjN3yUsgyoLw8jddDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTKgPs/DUNY4ugdkCAOD8d3Y+npJog0A+dvN2K0urbyctz7S2JdkA6D+/gfF/xlkPPakdXTwEGUA2N9IAQY2jFgDQPEN8jeGa4yjFuJNSEDACPYrmk2wNCDrllMCUoPVgPr6WEljBoY7MD/LeuQVwbyCFA7/GGQ9diMbPsQyEzYMAEBSiTlCp4U5AAAAAElFTkSuQmCC)
называется
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADsSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzPQ7YIqPgfEP8H0cbRDT4g8Rw32WKYGAOD7GuPvHpDorzZEG3sA9TwBllDeXmslDEDwx1Zj7wiksKsoyONx0OGYY+sW04xxKA0Xg85k5mx9fWSZEUA2FsyHnvS6tMkPWVlVyC7kmTDIF4FhRFq+JBlGDSM7sIigGzDIAYZ7zIyYtjNYBy1kGzDYAaBAhuSHIzv4gp4vIYhGwTi1+d5GMoyyN4kKcxAKbo+0tgX3RXgJAFJIiXoqR6rYfX1sZKgxAhN9f9giRJdHF+sMgy9UoMcDACUFMZYCDHBTwAAAABJRU5ErkJggg==)
-перестановочной с
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADuSURBVDjLvZNNCoMwEIWne3sAxRxC5g6ShT1ADW5diQsVsozuPIbew4sU6gnaM9gm/rQKtgZKFR6SxXx5741CURTwi+AvAPkc1qQNYAiVHOikHuO7A/TrNchHa5FLUgBsAyFMIQITAVoF0Qb4CPU0UJahQW1owKZNWJbGJmC6EVnuqTPn4bEHIKu0HOQMvd4+55bK3bsBvKo4WoAh/1ieFJ7FSXsLU17iRmkfJ6YOAbjLc6YFGAbIhcbCWRQ6bmQTIO1n87ZfBa5sYAFQGTkPLNW+sjt9fcPt0BEaJ18jxJQk8+LeIrd5nH1+pl0BT+oZdGtc7yckAAAAAElFTkSuQmCC)
, если в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADsSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzPQ7YIqPgfEP8H0cbRDT4g8Rw32WKYGAOD7GuPvHpDorzZEG3sA9TwBllDeXmslDEDwx1Zj7wiksKsoyONx0OGYY+sW04xxKA0Xg85k5mx9fWSZEUA2FsyHnvS6tMkPWVlVyC7kmTDIF4FhRFq+JBlGDSM7sIigGzDIAYZ7zIyYtjNYBy1kGzDYAaBAhuSHIzv4gp4vIYhGwTi1+d5GMoyyN4kKcxAKbo+0tgX3RXgJAFJIiXoqR6rYfX1sZKgxAhN9f9giRJdHF+sMgy9UoMcDACUFMZYCDHBTwAAAABJRU5ErkJggg==)
найдется такой элемент
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAANCAYAAACZ3F9/AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACWSURBVCjPY2hsbGQgB6NyGBgYYRiZT1BjjptsMVDhP1m3HBDNGGXMsJBB1mN3WkcHD16NIFyf52EoK+uxMtpDtt44usGHKKeCcEdHGo+HDMMekK1E+xGGQU7EZxtWjeXlsVIesrIribYRFoLRxsb10XkeXiB/ZmW52HlE1tvh1QgLUZATwf6UZdiNK0Rx+pHkBDC4NQIAm0P/y8bQ2yMAAAAASUVORK5CYII=)
, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE0AAAAUCAYAAADIiLCPAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAH+SURBVFjD7VhLbsIwFHzdlwOA8CHou0JlZQEHCBE7lEWFsqFSFlVr2GXR3oEue4ZygR6hEjlBe4bQOInBhHwcsGmlBumJKLHsmbFnXhRYLpfQVrNqRWhFa0X736LFvyte4vrXyGrCoQ1IvuQxDsIKcPy6cHAIgJsJY11TglwCR6PBD3e3N0i96REQgCiubfYfcWBHgC3CCI5fTJ0iUziKOCuD8n23Y/Vhjc5imH82o2Qe71zId46xSRcBQg5YHuNRnFoeG5i0n24cZZyVAY0R+K5ti0RLnmXggsC95gtB31q7QXCdLj7pWYS8oc1GJkXTjaOMsxIYngFI6SMB8pnfJbGjYmKxO4DOKnnuWQMC+GEzexCP2xA6mzfJpLJ8ypcuHCqcawVLFkPnOQvPMB+eu/u+3+PE0t1pHrJSJhVXRr6KpA4cKpxrPU2RPrm+32E2joomSHNkT860Bavz7HwcKpxVPB3tupKUD3JuiKOeWgC+646+bnvqxFHHuVK0xNNSACaT5SZIwR16PrNFeEl76sKhwrlUNP5uwj1d1pkOLHHQnbLwLVjIuDXPxKHK+Ug0boHEx7nFBIj4uN8Lm/D2zbuVuLcPX4hOscWpdS6OJpyPRMta9kbYQSyYdhDJJsR652/VxTYiX6ZfYKvCvymOJpxlQduvFu2noVa0P1s/CJd3gY4Zo5IAAAAASUVORK5CYII=)
. В работе найдены новые описания нильпотентных и сверхразрешимых групп на основе условия
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADsSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzPQ7YIqPgfEP8H0cbRDT4g8Rw32WKYGAOD7GuPvHpDorzZEG3sA9TwBllDeXmslDEDwx1Zj7wiksKsoyONx0OGYY+sW04xxKA0Xg85k5mx9fWSZEUA2FsyHnvS6tMkPWVlVyC7kmTDIF4FhRFq+JBlGDSM7sIigGzDIAYZ7zIyYtjNYBy1kGzDYAaBAhuSHIzv4gp4vIYhGwTi1+d5GMoyyN4kKcxAKbo+0tgX3RXgJAFJIiXoqR6rYfX1sZKgxAhN9f9giRJdHF+sMgy9UoMcDACUFMZYCDHBTwAAAABJRU5ErkJggg==)
-перестановочности для
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальных подгрупп. В частности, доказано, что:
Группа
нильпотентна тогда и только тогда, когда для любой
-максимальной подгруппы
группы
, имеющей непримарный индекс, в
найдется такая нильпотентная подгруппа
, что
и
-перестановочна со всеми подгруппами из
.Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAYCAYAAADzoH0MAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACtSURBVDjLY2hsbGSgBDMMMwOAgBEfxmtAjptsMVDRPyD+D6UxsKxbTjFeF9TXx0oaMzDcNY5u8EFX2BBt7EORASA5N7e8MLINICoQRw0gzoCOjjQeN2O32rSODh4MA8rLY6VABgDjuwRnykNLldhSIhTLvvbIqzdENyDKmGEhg4zHHqwuIAaDUiSyF0k2INrYuD62vl6SLANAgWxkFNVAdnkAcj56rhxuRRo5GAAZAiM6S0VN7wAAAABJRU5ErkJggg==)
- набор всех
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAARCAYAAAAPFIbmAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACISURBVCjPY2hsbGQghBnIUgQEjCCMV1Geh2wRA4Pxndj6eknyrcNmFYqi+vpYSWMGhjtARf+Noxt8cJrU0ZHG4y5nPAvZPRiK6vM8DGWNo3rxuinHTbZY1i2nGKcikFUesrIrPfLqDfE63IjBaHdsrFsYukI4oyHa2Afos38MxtELqBN3tFUEAK6029FgX+TpAAAAAElFTkSuQmCC)
-максимальных подгрупп группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD3SURBVDjLY2hsbGSgFDMMDUOAgBEdw8SJMgSkMMqYYSGQ/gfHxlELy8vTeN2M3WrTOjp48BpSH2nsC9Yk67EbWXFDtLEPSFzWLacYr0tgBhhHN/hgsyDHTbYYXQ5FQXWWi5EsA8MbBuPoBbi8medhmuyRV2+I0xBIGBjfja2vlyQmgDEM6ehI4/GQYdjDIOOxBzkcwOKyDLuhgfsfQhvfQbYIERb1sZLGDAx3QTGAzRvQQP2PHqgkGQIKUGxexQiTaGOGBQwMsm9csqqNkMXhXsVhAWr0QlxzB2xjebkULBBhsYYr2rFGI8RFSCkVS8IbgrmYroYAAB5dvjyoS1hPAAAAAElFTkSuQmCC)
.
Как показывают упомянутые выше результаты работ, условия перестановочности, накладываемые на подгруппы из
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAXCAYAAADpwXTaAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC3SURBVDjLY2hsbGSgFmYYYYYBASMxmCjD8jxki4CK/wHxfyiNgWXdcoqJ9mZ9faykMQPDXePoBh90hQ3Rxj5UMwwk5+GRF0oVw0iOzVHDsKZHigyDyt/BleZQbCwvj5UCGQZUWILN5jwPj9DY+npJkKFGDEa7QWxCOQCKZV975NUb4vJulLFsL7o82Zk62sMjOa2jg4diw0BZC1u4khb1wHCsjzT2ZTCKWkQwNglh9HBFd90IKbYBbihnzq9nEgAAAAAASUVORK5CYII=)
, существенно определяют строение основной группы. В работе Л.Я. Полякова было доказано, что группа
![](data:image/png;base64,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)
разрешима, если любая подгруппа из
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAYCAYAAADzoH0MAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACtSURBVDjLY2hsbGSgBDMMMwOAgBEfxmtAjptsMVDRPyD+D6UxsKxbTjFeF9TXx0oaMzDcNY5u8EFX2BBt7EORASA5N7e8MLINICoQRw0gzoCOjjQeN2O32rSODh4MA8rLY6VABgDjuwRnykNLldhSIhTLvvbIqzdENyDKmGEhg4zHHqwuIAaDUiSyF0k2INrYuD62vl6SLANAgWxkFNVAdnkAcj56rhxuRRo5GAAZAiM6S0VN7wAAAABJRU5ErkJggg==)
перестановочна со всеми подгруппами из
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAZCAYAAADTyxWqAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADQSURBVEjHY2hsbGSgFmYYYYYBASMxmCjDctxki4GK/wHxfyiNgWXdcoqJ9mZ9faykMQPDXePoBh90hQ3Rxj5UMwwk5+aWF0YVw0iOzVHDsGtGS3cUGRZtbFwXW18viTUHlJfHSoEMA6anEoKpHYs8thwAxbKvPfLqDbEZ1NGRxuMhy7Ab3QdkZ+r6SA87dMvINizawyM5raODh2LD6vM8DGWNo3opKs9ggQ4KX2wxTrRBoEB3M3arTatPk/SQM5mJnCTIclm0McMCfLE8QioUAArDpc6TNKOJAAAAAElFTkSuQmCC)
для всех
![](data:image/png;base64,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)
, где
![](data:image/png;base64,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)
. В связи с этим результатом естественно возникает вопрос о полном описании групп с таким свойством. Решению данной задачи и посвящена настоящая глава.
Отмеченные выше результаты работы допускают следующие уточнения.
[2.1]. Пусть
- группа,
- ее подгруппа Фиттинга. Если любая
-максимальная подгруппа группы
-перестановочна со всеми максимальными подгруппами группы
, то группа
метанильпотентна. Доказательство. Предположим, что теорема не верна, и пусть
![](data:image/png;base64,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)
- контрпример минимального порядка. Доказательство разобьем на следующие этапы.
(1) Для любой неединичной нормальной в
подгруппы
факторгруппа
метанильпотентна. Рассмотрим факторгруппу
![](data:image/png;base64,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)
. Пусть
![](data:image/png;base64,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)
- произвольная максимальная в
![](data:image/png;base64,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)
подгруппа и
![](data:image/png;base64,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)
- произвольная
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальная
![](data:image/png;base64,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)
подгруппа. Тогда
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADbSURBVDjLzZNBCoMwEEWney+gmEPI3EGysAeoIVtX4qIKWUZ3OYbew4t04Q16htqoGwkxTaEtDQyBR3jwZybQdR18quDrMn1OZrm4U8YQev3woWtebkKrq4u/jFmmpAYgd1rJxIc7ZTnCAJgPvvxQJiUPEWBC1mY+3ClrGWYAOHEhon2z5QXPK5cy9JatUbZGmzUfRbTKlCoCGsNI0rJ+J6JVJiuaECA3c1pbdPsUD2V69A3EdCyUCny4VbY0WAgeLVF0xGa/9TbulG3LuGs2st7Gza3/7Uf/C9kTlXm3FqepImkAAAAASUVORK5CYII=)
максимальна в
![](data:image/png;base64,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)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальна в
![](data:image/png;base64,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)
, а значит, по условию подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADnSURBVDjLY2hsbGSgFmagi2FAwIiMCYnjNSzHTbYYqPgfEP8H0cbRDT5I4v8hcrKvPfLqDYnyZkO0sQ9QwxtkDeXlsVLGDAx3ZD3yikgKs46ONB4PGYY9sm45xRCD0ng95ExmxtbXS5IVAWBvyXjsSatPk/SUlV2B7EqSDYN4FRRGqOFDlmHQMLoLiwCyDYMYZLzLyIhhN4Nx1EKyDYMZBApsSHIwvosr4PEahmwQiF+f52EoyyB7k6QwA6Xo+khjX3RXgJMEJImUoKd6rIbV18dKghIjNNX/gyVKdHF8scow9EoNcjAAh7zGVVhoTpgAAAAASUVORK5CYII=)
-перестановочна с подгруппой
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAARCAYAAAAG/yacAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADGSURBVDjLY2hsbGQgFTNQrAkIGAlhDE1RxgwLgRL/kPB/FL5x1EIUTR0daTweciYzY+vrJUH8HDfZYgYZjz1pHR08ML5xdIMPiqb6PA9Dj8h6O7gBMgx7ZN1yiuHykZGGMAOxehRkgCyD7E2PvHpDokMP7DQG47swkwlqgjkN5mmiNNXXx0oaMzDchXmaKE0N0cY++JyGVRM4rvA4DUUTKLars1yMZBkY3hhH1vvCYh+nJrDnZRl2o8S+rMduWMRSP8HSVBMASkkvdXoZyhkAAAAASUVORK5CYII=)
. Но тогда, согласно лемме , подгруппа
![](data:image/png;base64,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)
-перестановочна с подгруппой
![](data:image/png;base64,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)
. Итак, условие теоремы выполняется в
![](data:image/png;base64,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)
. Но
![](data:image/png;base64,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)
и поэтому согласно выбора группы
![](data:image/png;base64,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)
, мы имеем (1).
(2)
- разрешимая группа. Если в группе
![](data:image/png;base64,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)
существует единичная
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC7SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvh5HrJFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs/zMJSV9VyR1tHBQ7RGUFREGcv2IvuZKI05brLF2JyIV2N9pLGvrFtOCSwRVGe5GHlE1tvh1AhSBNIEijtUbHwXFrdYNUIj/B8GNo5eQNtETlONAMd4UB5pSxCHAAAAAElFTkSuQmCC)
-максимальная подгруппа, то теорема очевидно справедлива. Предположим, что в группе
![](data:image/png;base64,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)
все
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgBzNQVSMQMMIw0RrLy2OljBkY7gA1/QNh48h6X4IaOzrSeDzkTGbG1tdLgvg5brLFQM3/jaMbfPBqrI/0sPPIqzdEMUiGYQ+DcdRCkgMnyphhIckaYTYSdCo6rs5yMZKV9VyR1tHBQ7RGUFREGcv2IvuZKI2gEMXmRLwa6yONfWXdckpgiQDkZI/IejucGkGKQJpAcYeKje/C4harRmiE/8PAxtELaJvIaaoRAKfWUA2TmaRHAAAAAElFTkSuQmCC)
-максимальные подгруппы отличны от единицы. Докажем, что для каждой максимальной подгруппы
![](data:image/png;base64,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)
группы
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Пусть
![](data:image/png;base64,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)
- максимальная подгруппа группы
![](data:image/png;base64,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)
. Тогда по условию для каждого
![](data:image/png;base64,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)
, мы имеем
![](data:image/png;base64,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)
. Ввиду леммы ,
![](data:image/png;base64,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)
и, следовательно,
![](data:image/png;base64,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)
. Значит,
![](data:image/png;base64,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)
. Поскольку
![](data:image/png;base64,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)
, то
![](data:image/png;base64,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)
и поэтому по выбору группы
![](data:image/png;base64,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)
мы заключаем, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAYCAYAAACMcW/9AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAI2SURBVFjD7VbBTgIxEK13vaux3PwAd+6eTO0Bryaw2ZOEAyE1AZM9qCncSPwDT/od8AP6DfgF8g3iTttZa9lFwEQhgWRCdnc6ffPezLSs3++zTbCNALkF+udAs99OaPTe9ylbs2jsXwHFAHVgz9n/R25Qf07T5p4Acd8cDHbRLwbQidYHtC4G9mT94c1/75uuwUXmM0U/LlVnZaAu0AfjckiA0HoxVE1w0e4aP50cAMQ6XG/9+EQqfRJ+u22dRZyxSZbIuCyRhYBSthD3qkUL2oJ36RsCKvKzSswCHQyau+dQeUSglOxKQPNsIX4qW6AENAhAKDuxLIS4BsbewiRwrRBwP4+IhYBaJmZrq6ip5skOSdIIgWolT0CoBioyr35/BIqyyCM2Ykdy5Nelec/Z0DXU1DXKOEmgUcQKslzT6hhjkbwYAxtQ9dS+2SNrypXHk2EoY6EsiGukKW1eJjuxbNRxsahckFUsrWVlXwqoL9lc2R0IAkqShzGWna2BbDgD+eSsdRuF3epLhpvLmj4tkp1AGFA8egWQD1RKPsshwHwkuvEXS3nllyCbkY6xsck6TQ8pO5oGxJYS4tJnBX3SNDmEyvljM033vFn6jpL7MTIQNyFjjul8rirJO+FBUFgPX6eLZ274G3ZB3vnZYuAvX7uhL/lMPG/8ITkRi4YEskz+f79sGOa9kspYf7fT5fvJtVZA8+dgRK4FUMsivFBPYMMVHa9rcdeky44124DbG/4W6KYB/QS61YhjT8TU7gAAAABJRU5ErkJggg==)
- разрешимая группа. Это означает, что
![](data:image/png;base64,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)
разрешима, и следовательно,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAATCAYAAAB2pebxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD4SURBVDjLY2hsbGSgFDMMDUOAgBEdw8SJMgSkMMqYYSGQ/gfHxlELy8vTeN2M3WrTOjp48BpSH2nsC9Yk67EbWXFDtLEPSFzWLacYr0ugBvw3jm7wwWZBjptsMbocioLqLBcjWQaGNwzG0QtweTPPzTjFI6/eEKchkDAwvhtbXy9JTABjGNLRkcbjIcOwh0HGYw9yOIDFZRl2QwP3P4Q2voNsESIs6mMljRkY7oJiAJs3oIH6Hz1QSTIEFKDYvIoRJtHGDAsYGGTfuGRVGyGLw72KwwLU6IW45g7YxvJyKVggwmINV7RjjUaIi5BSKpaENwRzMV0NAQAYqL46wntofwAAAABJRU5ErkJggg==)
- разрешимая группа.