Лемма доказана.
2.2 Супердобавления к максимальным подгруппам
Теорема 2.2.1 Пусть
– максимальная подгруппа группы
. Подгруппа
обладает супердобавлением в группе
тогда и только тогда, когда индекс
в
есть простое число. Доказательство. Необходимоcть. Пусть
![](data:image/png;base64,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)
– максимальная подгруппа группы
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
имеет супердобавление в группе
![](data:image/png;base64,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)
, т.е. существует такая подгруппа
![](data:image/png;base64,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)
из
![](data:image/png;base64,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)
, что
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
есть собственная подгруппа в
![](data:image/png;base64,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)
для каждой подгруппы
![](data:image/png;base64,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)
из
![](data:image/png;base64,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)
, отличной от
![](data:image/png;base64,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)
. Пусть
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
– две различные максимальные подгруппы в группе
![](data:image/png;base64,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)
. Тогда
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. Из максимальности
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADkSURBVDjLY2hsbGSgFmaguWFAwAjETEiYEZ84XsOijRkWABX+A+L/QPxX1iOvCJ84QW/muMkWMzDIvvbIqzckRhyvYVHGDAsZjKMXECuO07D6+lhJYwaGu8bRDT7EiOM3LNLYl4HB+G5oebk0coBDxe/E1tdLEm0Y2CuQgP6Lhv/j8iJWwzo60ng8ZBj2oMcUIS9iNaw6y8VIlkH2JnpsNUQb+wBj8Q22WMRpGDDqSxhkPXandXTwECOO1TBQai4vD5UGeUXWLacEOdVjE8drWJ6HbBFKYEMDGl0cPSzpm9EHhWEAXpq2990nPYMAAAAASUVORK5CYII=)
следует, что
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
являются подгруппами
![](data:image/png;base64,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)
. Но тогда
![](data:image/png;base64,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)
, противоречие с тем, что
![](data:image/png;base64,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)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADjSURBVDjLY2hsbGSgFmaguWFAwAjETEiYEZ84XsOijRkWABX+A+L/QPxX1iOvCJ84QW/muMkWMzDIvvbIqzckRhyvYVHGDAsZjKMXECuO07D6+lhJYwaGu8bRDT7EiOM3LNLYl4HB+G5oebk0coDDxGPr6yWJNgzsFUhA/0XD/3F5EathHR1pPB4yDHvQY4qQF7EaVp3lYiTLIHsTPbYaoo19gLH4Blss4jQMGPUlDLIeu9M6OniIEcdqGCg1l5eHSoO8IuuWU4Kc6rGJ4zUsz0O2CCWwoQGNLo4elvTN6IPCMABhaLb46r0WOgAAAABJRU5ErkJggg==)
– максимальная в
![](data:image/png;base64,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)
подгруппа. Следовательно, в
![](data:image/png;base64,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)
имеется единственная максимальная подгруппа
![](data:image/png;base64,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)
. Если
![](data:image/png;base64,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)
, то циклическая подгруппа, порожденная элементом
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC1SURBVDjLY2hsbGQgFTMMjCYgYARiJhDGIsaIVVNDrLE3UPIvA4Psa5esaiOQwvpIY1+wmKzH7rSODh6czsvzkC1iMIpalOMmW8xgHL2AKD/V53kYyjIwvJF1yykmOiDKy9N4PWQY9hhH1vsSpQnkjzw34xQTE9nlDMZRC2FiWDXBQgnkcVmPvCKwE2U9VoampfGBDPHIqzfE0AT2PCiUoB7v6Ejj8ZBl2A0SAxkyCFIETTUBANpVDITwAQUIAAAAAElFTkSuQmCC)
, не содержится в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAYAAAALHW+jAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFUSURBVEjH7ZVBToNAFIZ/uq7dN2W8gzyP0ABN65JES9jOomlYVBMWTQR2nEEXmi6JJ6jt3isY7A16hVZnajFIFZG6MNHFC+ExfPPez/sHhGGInwz8A1+TgCKilgllNx/XSgNdk43ESysRz/LKTHeUya83z5gx5VFUL91yYFNPFLQmJ+jK+1hUNR60NQZ6cHy/+W0Nhzq7ADPvZRWyRZtw+1lVXwKjiNdNFTOmD889z2oRkKSVVvoovmseMbBHXadLgJKiFssBz+hEiq+ALduDMe09Nn0NExx37joMUwW0sDyvVRno+05TaLYgO+hJLSUUqjGzOG/k18bbmSwGbtqlp1S37QZJHvq2WWbtO6B0AedWQ1cxh3Y6SZ0g82L+iAFLqPpcQlPnSKhxSFcfAgOHult3rLJO2MlnnFMIrBK/H+h5/EAAr7NjtRewT7jJnzx/8BfwAmzIhVBZkC/oAAAAAElFTkSuQmCC)
, поэтому
![](data:image/png;base64,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)
. Кроме того,
![](data:image/png;base64,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)
– примарная группа, то есть
![](data:image/png;base64,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)
. Если
![](data:image/png;base64,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)
– максимальная подгруппа в
![](data:image/png;base64,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)
, то индекс
![](data:image/png;base64,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)
в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEuSURBVDjLxZNBTsJAFIb/sibskb5D2OcRyFCCLpuopNtZNIQFmsyCxNJdj2FYEk+AsPcKBjmBHkHReeAkCEmtGmKTP5O+mXzvzd+/yLIMfxUOBrGPZ1XZkrdfn1QKIUlIA3vwzepdVgqTgdT7m/pqvUetqc7zauF1Rl0+tY1XHI868j6x3YdJMyDwQ5ym9VKe9BRdg8J76Sbjdxm3292/heS5roY+ZqR6V8ZEDQYWbqLSxqb98JhAj0rxDcCL3fHLQS74TAz0QM/NZMi/+sSXAcY4ad+1CVMPvIyMafwIYkx8ZD1YigfijYDgt2aR1rXSkM1V+Mn5kKZxXYwtAn1JqdZRTfmYIzgfu0RK3eaDCXiBr+YCcgneg4xi7nymVPTqMrFTX++5BB/+B/wXyAd8LIlAbELO4AAAAABJRU5ErkJggg==)
есть простое число
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADxSURBVDjLY2hsbGSgBDPQxAAgYIJixlUINhNRBtTneRjKMjC8Amr4ZxxZ7xttzLAAyP7LyGB8N7a8XIooF9TXx0oaMciekpNjuG4c2+Dd0ZHG4yHDsEfWLaeYOAMijX0ZZI1PRubVq4L4cAM88oqIMiDKmGGhcXSDD4xfneViJMcgd8Mjr96QcBiAnW+0O7a+XhLEBwVihBHDIgbj6AVEBSLINllZj1WhaWl8oJCPNGZayMBgfBtmIEEDctxkS0ChDsfGUfOJTgfgwJKVXYnNrwQNAPkV6HxjmPNJNgAY8vPhzpZ135XW0cEzcHlhaBkAAHQ7gLaXyiXAAAAAAElFTkSuQmCC)
и
![](data:image/png;base64,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)
– подгруппа в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGSgFmaguWGrGBiYGFAxIz5xvIZFGTPMByr8B8T/gfivrEdeET5xgt7McZMtZmCQfe2RV29IjDhew6KMGBYxGEcvIFYcp2H19bGSxgwMd42jG3yIEcdvWKSxLwOD8d3Q8nJp5ACvjTT0A4rfia2vlyTaMGBAL4QG9F80/B+XF7Ea1tGRxuMhw7AHPaYIeRGrYdVZLkayDLI30WOrIdrYBxiLb7DFIk7DgFFfwiDrsTuto4OHGHGshoFSc3l5qDTIK7JuOSUMDKuYsIujpnqshuV5yBahBLZx1Hxs4uhhSd+MPigMAwAOCbjv7P8bIwAAAABJRU5ErkJggg==)
. Поэтому,
![](data:image/png;base64,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)
.
Достаточность. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADjSURBVDjLY2hsbGSgFmaguWFAwAjETEiYEZ84XsOijRkWABX+A+L/QPxX1iOvCJ84QW/muMkWMzDIvvbIqzckRhyvYVHGDAsZjKMXECuO07D6+lhJYwaGu8bRDT7EiOM3LNLYl4HB+G5oebk0coDDxGPr6yWJNgzsFUhA/0XD/3F5EathHR1pPB4yDHvQY4qQF7EaVp3lYiTLIHsTPbYaoo19gLH4Blss4jQMGPUlDLIeu9M6OniIEcdqGCg1l5eHSoO8IuuWU4Kc6rGJ4zUsz0O2CCWwoQGNLo4elvTN6IPCMABhaLb46r0WOgAAAABJRU5ErkJggg==)
– подгруппа группы
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADtSURBVDjLY2hsbGSgBDPQxAAgYARiJmyYKAMaYo29gYr/AvF/KA3GjAzGd0PLy6WJ8kJ9noehLAPDG+PYBm8Qv6MjjcdDlmE3g4zHnrSODh7CBkQa+zIwGN+Jra+XhInluMmWAMXuIovhNCDKiGERg3H0Ahgf6BfGCJCYrMdugi4oL4+VMmZguGsYWesHDTzmLLDtDH9hXsJrAMT5jP+QAvAP0Om3kZ2O14AoLE4lOh3U18dKgpwv65FXRFZCqs5yMZJjkLvhUdxgQLIBoAADh7RRxCIGhlVMJBkATTiv4IEm676LrDAYHLmRFAwAnGF5zpX0ZbkAAAAASUVORK5CYII=)
– силовская
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADxSURBVDjLY2hsbGSgBDPQxAAgYIJixlUINhNRBtTneRjKMjC8Amr4ZxxZ7xttzLAAyP7LyGB8N7a8XIooF9TXx0oaMciekpNjuG4c2+Dd0ZHG4yHDsEfWLaeYOAMijX0ZZI1PRubVq4L4cAM88oqIMiDKmGGhcXSDD4xfneViJMcgd8Mjr96QcBiAnW+0O7a+XhLEBwVihBHDIgbj6AVEBSLINllZj1WhaWl8oJCPNGZayMBgfBtmIEEDctxkS0ChDsfGUfOJTgfgwJKVXYnNrwQNAPkV6HxjmPNJNgAY8vPhzpZ135XW0cEzcHlhaBkAAHQ7gLaXyiXAAAAAAElFTkSuQmCC)
-подгруппа группы
![](data:image/png;base64,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)
. Тогда
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADmSURBVDjLY2hsbGSgBDPQxAAgYARiJmyYKAMaYo29gYr/AvF/KA3GjAzGd0PLy6WJ8kJ9noehLAPDG+PoBh8Qv6MjjcdDlmE3g4zHnrSODh7CBkQa+zIwGN+Jra+XhInluMkWA8XuIovhNCDKiGERg3H0AuRwiQCJyXrsJuiC+vpYSWMGhruGkbV+sMAD2l4CCgfj2AZvgmEAcT7jP+QABDr9NrLT8RoQhcWpRKcDmPNlPfKKyEpI1VkuRnIMcjc88uoNSTYAFFjgkDaKWMTAsIqJJAOgCecVPNBk3XeRFQaDIzeSggEaAnjax7l4+QAAAABJRU5ErkJggg==)
не содержится в
![](data:image/png;base64,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)
и существует элемент
![](data:image/png;base64,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)
. Пусть
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Ясно, что
![](data:image/png;base64,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)
, поэтому
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. Теперь
![](data:image/png;base64,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)
принадлежит
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGSgFmaguWGrGBiYGFAxIz5xvIZFGTPMByr8B8T/gfivrEdeET5xgt7McZMtZmCQfe2RV29IjDhew6KMGBYxGEcvIFYcp2H19bGSxgwMd42jG3yIEcdvWKSxLwOD8d3Q8nJp5ACvjTT0A4rfia2vlyTaMGBAL4QG9F80/B+XF7Ea1tGRxuMhw7AHPaYIeRGrYdVZLkayDLI30WOrIdrYBxiLb7DFIk7DgFFfwiDrsTuto4OHGHGshoFSc3l5qDTIK7JuOSUMDKuYsIujpnqshuV5yBahBLZx1Hxs4uhhSd+MPigMAwAOCbjv7P8bIwAAAABJRU5ErkJggg==)
, следовательно, если
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoTwvlc5Nh2Gsc3eBDsgEgZ0cZMywE0v9JNgCkuT7S2NfYza1WlkH2pkdevSFJBoD8LWsc3dMQbezDwGB8N7a+XpJoA8D+NnarC01L46uNNPQjyQCQ06ONGRYA6b8gzMjA8I9BxmNPWkcHD0ED4P6ObfCGiYEDkRgDQJph/kYWBxtgHL0Ab0oEAiawX2Xc9qaVl/PCDEyDpgFZt6wSBoZVTFgNqK+PlTRmYLgN9fMfWY+sIpB4Q6yxNywcQOIMsu67kL3BMPRyIzoGAAq4fmgf1ilPAAAAAElFTkSuQmCC)
– собственная подгруппа циклической группы
![](data:image/png;base64,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)
, то
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVDjLY2hsbGSgBDPQ3QAgYCTbgOosFyNjt7wUsgwoL0/jdZNh2Gsc3eBDsgEgZ0cZMywE0v/JMqA+0tjX2M2tVpZB9qZHXr0hSQaA/C1rHN3TEG3sw8BgfDe2vl6SaAPA/jZ2qwtNS+OrjTT0I8kAkL+jjRkWAOm/IMzIwPCPQcZjT1pHBw9RBoD9HdvgDeODA5EYA0A2w/yNLA42wDhqId6UCARMYL/KuO1NKy/nhRmYlhbKB0oDsm45JQwMq5iwGlBfHytpzMBwG+ZnWY+8IpB4Q6yxN0wMjGXddyF7g2Ho5UZ0DABRWIG2vnPnxwAAAABJRU5ErkJggg==)
– подгруппа в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADkSURBVDjLY2hsbGSgFmaguWFAwAjETEiYEZ84XsOijRkWABX+A+L/QPxX1iOvCJ84QW/muMkWMzDIvvbIqzckRhyvYVHGDAsZjKMXECuO07D6+lhJYwaGu8bRDT7EiOM3LNLYl4HB+G5oebk0coBDxe/E1tdLEm0Y2CuQgP6Lhv/j8iJWwzo60ng8ZBj2oMcUIS9iNaw6y8VIlkH2JnpsNUQb+wBj8Q22WMRpGDDqSxhkPXandXTwECOO1TBQai4vD5UGeUXWLacEOdVjE8drWJ6HbBFKYEMDGl0cPSzpm9EHhWEAXpq2990nPYMAAAAASUVORK5CYII=)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADkSURBVDjLY2hsbGSgFmaguWFAwAjETEiYEZ84XsOijRkWABX+A+L/QPxX1iOvCJ84QW/muMkWMzDIvvbIqzckRhyvYVHGDAsZjKMXECuO07D6+lhJYwaGu8bRDT7EiOM3LNLYl4HB+G5oebk0coBDxe/E1tdLEm0Y2CuQgP6Lhv/j8iJWwzo60ng8ZBj2oMcUIS9iNaw6y8VIlkH2JnpsNUQb+wBj8Q22WMRpGDDqSxhkPXandXTwECOO1TBQai4vD5UGeUXWLacEOdVjE8drWJ6HbBFKYEMDGl0cPSzpm9EHhWEAXpq2990nPYMAAAAASUVORK5CYII=)
обладает супердобавлением
![](data:image/png;base64,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)
в группе
![](data:image/png;base64,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)
.
Теорема доказана.
Следствие 2.2.2 Группа сверхразрешима тогда и только тогда, когда все ее максимальные подгруппы имеют супердобавления.
Доказательство. Если
![](data:image/png;base64,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)
– сверхразрешимая группа, то все ее максимальные подгруппы имеют простые индексы. По теореме 2.2.1 все максимальные подгруппы обладают супердобавлениями.
Обратно, пусть все максимальные подгруппы имеют супердобавления. По теореме 2.2.1 все они имеют простые индексы. Следовательно группа
![](data:image/png;base64,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)
сверхразрешима.
Следствие доказано.
Следствие 2.2.3 Пусть
– некоторое множество простых чисел. Если в
-разрешимой группе
каждая максимальная подгруппа, индекс которой делится на простое число из
, имеет супердобавление, то
–
-сверхразрешима. Доказательство. По теореме 2.2.1 индекс каждой максимальной подгруппы из
![](data:image/png;base64,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)
либо
![](data:image/png;base64,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)
-число, либо равен некоторому простому числу из
![](data:image/png;base64,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)
. Группа
![](data:image/png;base64,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)
-сверхразрешима для всех
![](data:image/png;base64,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)
. Поэтому
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAPCAYAAAA71pVKAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADySURBVDjLY2hsbGQgFzNQXfMqBgYmBgYGZux4FRNOzWlpoXyesgy7GBkY/gEV/wFhKPsvmG8cNR+r5o6ONB5PWdnlHnn1htHGxvWx9fWSIDEPWdmVIDG8zq7Pi1SNzKtXLS+PlTI2jq4DiVVnuRjJynquSOvo4CHKzzluxqkwm6KMGRYaxzZ4ExVgIFtN5DxmgmwCsY0YjHaDnE9QMxAwZrnJlsBsqo809mUwjl4AkfvPiFMzSGNtpKEfg6znLpj/oo0ZFsi6ZZSWl4dKw8IAq+aGYg8DOQa5ax7FDQYwsSwP2SJIdBndwuZ0hsGVPOmiGQCM5Dk7SqH4tQAAAABJRU5ErkJggg==)
-сверхразрешима.
Следствие доказано.
Следствие 2.2.4 Если подгруппа
имеет супердобавление в группе
и
– подгруппа группы, в которой
является максимальной подгруппой, то
– простое число.