(5)
![](data:image/png;base64,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)
,
где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADjSURBVDjLY2hsbGQgBzNQVSMQMAIxEzaMV2NDrLE3UNFfIP4PpcGYkcH4bmh5uTRep9bneRjKMjC8MY5u8AHxOzrSeDxkGXYzyHjsSevo4MGtMdLYl4HB+E5sfb0kTCzHTbYYKHYXJIZTY5QRwyIG4+gFyP6OAInJeuzGaWN9faykMQPDXcPIWj9YoABtKwH50zi2wRunHyHOZPyHHDBAJ95GdjZuZ0KdRHQ8wpwp65FXRFICqM5yMZJjkLvhkVdvSLRGUCCAQ84oYhEDwyomojRCI/wVPDBk3XeR5MeByR3EYABzX0V00l1HGwAAAABJRU5ErkJggg==)
- группа порядка
![](data:image/png;base64,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)
, каждая подгруппа которой нормальна в группе
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
- циклическая
![](data:image/png;base64,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)
-группа и
![](data:image/png;base64,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)
;
(6)
![](data:image/png;base64,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)
,
где
![](data:image/png;base64,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)
- примарная циклическая группа порядка
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
- группа простого порядка
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD+SURBVDjLY2hsbGQgBzNQXWMoAwMzAxj/Z1zFwMAEZDPi1QhSUF4eKm3MwHgHyP4j65ZTHGHEtMg4tsEbr8bqLBdjWQbG17IeWUUgfo6bbDEDg/Gd2Pp6SZway8vTeN1lGPcwGEfNh4nVRxr7MhhHL8DrR7AiJNM7gAa5yTDsNY5u8MGrMcqYYSHQtoUwvwKdWcLAIPvaI6/eEK/GaGOGBQxGEYtAoQmyXdbEZLmsrOeKtI4OHrwaG4o9DOQYGF6CQhPkT5CNsh55RSTFY0dHGo+HrOxKbM7EqREU+Xl5oTJGDEZ7QsvrpYnSWF8fK2nEwHAL7Fyok+mTVgefRgAoBE5onQ0lPAAAAABJRU5ErkJggg==)
, где
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
;
(7)
![](data:image/png;base64,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)
,
где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADjSURBVDjLY2hsbGQgBzNQVSMQMAIxEzaMV2NDrLE3UNFfIP4PpcGYkcH4bmh5uTRep9bneRjKMjC8MY5u8AHxOzrSeDxkGXYzyHjsSevo4MGtMdLYl4HB+E5sfb0kTCzHTbYYKHYXJIZTY5QRwyIG4+gFyP6OAInJeuzGaWN9faykMQPDXcPIWj9YoABtKwH50zi2wRunHyHOZPyHHDBAJ95GdjZuZ0KdRHQ8wpwp65FXRFICqM5yMZJjkLvhkVdvSLRGUCCAQ84oYhEDwyomojRCI/wVPDBk3XeR5MeByR3EYABzX0V00l1HGwAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
- группы простых порядков
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADoSURBVDjLY2hsbGQgBzNQVSMQMEExIxSD+Xg11ud5GMoyMLwCKvxvHFnvG23MsADI/svAYHw3trxcCq+N9fWxkkYMsqfk5BhuGMc2eHd0pPF4yDDskXXLKcavMdLYl0HW+GRkXr0qiA/X6JFXhFdjlDHDQuPoBh8YvzrLxUiWQfamR169IW4/gp1ptDu2vl4SGlCMIIMYjKMX4A0csOmyHqtC09L4QCEJ1sRgfBtmEE6NOW6yxZBQhGI0m7BqBAeCrOxKZL8QTAAgvwCdaQxyZlp5OS/RGhERDcSyHrvTOjp46JdWB6dGACARS4cPViE7AAAAAElFTkSuQmCC)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADtSURBVDjLY2hsbGQgBzNQXSMQMEEx4yooTVBjeXmotDEDwx2g4r+ybjnFEUYMi4yjG3zwaqzOcjGSZWB8LeuRVwTi57jJFjMwGN+Jra+XxKmxvDyN112GYQ+DcfQCmFh9pLEvMh+rRrAiJNNhBqE7E0NjlDHDQgbjqIXQwGEEOrOEgUH2tUdevSFejdHGDAsYjCIWgUITZLusiclyWVnPFWkdHTz4nZrnYSjLwPAKFJoMxpELQDbCAonoeOzoSOPxkJVdic2ZODWCnAqKSyMGoz2x5eVSRGmsr4+VBEb+bbBzwU6Omk+ftDr4NAIA8sFOPQSqDIcAAAAASUVORK5CYII=)
(
![](data:image/png;base64,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)
),
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADuSURBVDjLY2hsbGQgBzNQVSMQMAIxExpmJKgx2phhAVDhPyD+D8R/wWyjqEXImnE6JcqYYSEDg/Hd2Pp6yYZoYx+QIcbRDT7EaTSOXgBi19fHShozMNyVdcspxqsRphBmQ3WWi5EsA8MbWY+8IrwaIU4zvhtaXi6dlhbK5yHDsIdB1mN3WkcHD16NOW6yJdDAgQQQ1Ml4Q7WjI40HZAPIWTCbQQFEUCPEP7I3PfLqDeF+jaz3JagR7Ewk/4DjFBiHODWCIre8PFQaGuwlsMiGOFf2jUtWtTHWBJDnIVsETSUQjBqHt5HFqJ/IaaoRAGC/REVE/RNNAAAAAElFTkSuQmCC)
- циклическая
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAOCAYAAAAbvf3sAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC0SURBVCjPY2hsbGQgBTNQpCGUgYGZAYxXMSH4EDaGhvr6WEkjBoZbjAwM/2TdcorL00L5PGQY9jAYRy/AaUN5eRqvhwzjHtPInEhPWdnlJiayy2Q9cgpxaqjOcjGSZTA65eZmXOtR3GBA0A85brIlDLKyN009cpKJ8nSUEcMiBlnPXWkdHTwENZSXx0oZMTDeNY5t8CYqWOsjjX0ZGIzvxNbXSxKlIcdDtpDBOGo+bWOaJhoAWr7v+REqeKIAAAAASUVORK5CYII=)
-подгруппа в
![](data:image/png;base64,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)
(
![](data:image/png;base64,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)
), которая не является нормальной в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADmSURBVDjLY2hsbGSgFDPQ3BAgYETGMDGiDAEprM5yMZJlYHgNZP8DY1mP3Wn1aZJuxm61aR0dPHgNKS9P4/WQYdjDwCD72iOv3hAmXp/nYQg21DhqIV6XwA0A2YpmGwjnuMkWG0c3+OA1BKQI6II3yC5AxvWRHnbY5OCMjo40HrArsDkXSwBjNaS+PlbSmIHhrqxbTjGygoZoYx9o4P6H0MZ3YuvrJUkyBFmOwTh6Ad50AvaOLMNuBhmPPWnl5byYrsEdVqg2IkUjchhEGTEswhVjWNMJ1Ol34IkMirFFLf3yztAzBADnvY8M78csLQAAAABJRU5ErkJggg==)
, но максимальная подгруппа которой нормальна в
![](data:image/png;base64,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)
.
Доказательство. Необходимость. Пусть
![](data:image/png;base64,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)
- ненильпотентная группа, у которой каждая 2-максимальная подгруппа группы
![](data:image/png;base64,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)
перестановочна со всеми 3-максимальными подгруппами группы
![](data:image/png;base64,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)
.
Если в группе
![](data:image/png;base64,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)
все максимальные подгруппы нильпотентны, то группа
![](data:image/png;base64,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)
является группой Шмидта. Ввиду леммы, группа
![](data:image/png;base64,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)
оказывается группой типа (1) или типа (2).
Итак, мы можем предположить, что в группе
![](data:image/png;base64,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)
существует ненильпотентная максимальная подгруппа.
Из теоремы следует, что группа
![](data:image/png;base64,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)
разрешима. Так как в разрешимой группе индекс любой максимальной подгруппы является степенью простого числа, то
![](data:image/png;base64,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)
.
I.
![](data:image/png;base64,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)
.
Пусть
![](data:image/png;base64,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)
- некоторая силовская
![](data:image/png;base64,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)
-подгруппа в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADmSURBVDjLY2hsbGSgFDPQ3BAgYETGMDGiDAEprM5yMZJlYHgNZP8DY1mP3Wn1aZJuxm61aR0dPHgNKS9P4/WQYdjDwCD72iOv3hAmXp/nYQg21DhqIV6XwA0A2YpmGwjnuMkWG0c3+OA1BKQI6II3yC5AxvWRHnbY5OCMjo40HrArsDkXSwBjNaS+PlbSmIHhrqxbTjGygoZoYx9o4P6H0MZ3YuvrJUkyBFmOwTh6Ad50AvaOLMNuBhmPPWnl5byYrsEdVqg2IkUjchhEGTEswhVjWNMJ1Ol34IkMirFFLf3yztAzBADnvY8M78csLQAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAUCAYAAAC9BQwsAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEuSURBVDjLzZMxbsJAEEW/SYvSo7B3SJgDpEFmJZQSKTZy62KFKACJgmLtzkXuEEiZIwRuArlAwhEgya7Bine9QREVxcjWzr6Z7z9jpGmKcwKXBb4CNZjhnQT1hTjuXXOGpXrfF8F8MSngCvStEsJn+sKeoqRbnCcRdT3giwL5UAF1tUEOsU8+Tm7toiFhgSZfxVlWNxIz0W4xYMv4cOT6hD/BsIUXgDaRlA0byrK4zptYgfGlAUoZNQh4B/Xnrm62ml9wyO/yhD8Yuwx7PKhZF2rsjhsFTuxZulw2KgvORp5ytC1mdBz4VUC1hXruypBzjgFhXhr6DhQ+/2vl9MYEgbjXHV0bVQH14XTau1Ea14dubFuWnLtK/acKqFeqcO3o8IchmXXe9Pwu9H88FT+oc3dIsGR55QAAAABJRU5ErkJggg==)
- некоторая силовская
![](data:image/png;base64,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)
-подгруппа в
![](data:image/png;base64,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)
, где
![](data:image/png;base64,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)
.
Предположим, что в группе
![](data:image/png;base64,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)
нет нормальных силовских подгрупп. Так как группа
![](data:image/png;base64,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)
разрешима, то в
![](data:image/png;base64,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)
существует нормальная подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEnSURBVDjLY2hsbGSgFDPQzBAgYIJiRmTxVQhxIF7FhNOQ+jwPQ1kGhleMDAz/ZN1ySpDloowZ5gMN+AfEfxmMo+YT9A5Qw0IGBuO7sfX1ksjiOW6yxcaxDd4EvVNeHitlYmIyw5iB4Y5xZL0vTLyjI43HzditNq2jg4egIQ3Rxj7G0Q0+eR6yRUBnL4SJV2e5GJl65CUTFbB5bm5hIG9Awkf2pktWtRFE3DjFI6/ekKAhICd7eEQnw9myDLtBAVxensaLzStYDQE52SOy3g7Zawwy7nuyslzssHkFqyHoTq6vj5UEBbCsrMl2bF5BMQSUsNLSQvmATq4LTUvjQ1YUbcywgEHWYzc2r6AY0hBr7A1ORAwMfxhk3XchawAFMC6v0DbvDF1DAJhhmp2zrzziAAAAAElFTkSuQmCC)
простого индекса, скажем индекса
![](data:image/png;base64,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)
, и она не является нильпотентной группой. Действительно, если
![](data:image/png;base64,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)
нильпотентна, то в ней нормальна силовская
![](data:image/png;base64,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)
-подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEiSURBVDjLY2hsbGSgFDPQzBAgYARiJiTMiEWcEa8heR6yRUBF/4D4P4iW9cgrAonnuMkWQ8X+Msh67krr6ODB652GaGMfkAHGsQ3eMFdUZ7kYyTIYn4itr5ckKkyAtpYwyHrsBtkGcn60McMCZNsJGtLRkcbjIcOwR9Ytp7i8PFTamIHhNsxFRAdsfZ6HoSyD7E03N+M6BgbjO+jOJ86QSGNfSMDKvnHJqjYiK4qjjBkWMph4rvGQZdgNdMnd2PJyKZIMqa+PlQSGwV3j6AYfcNiADJLx2JNWXs5LvCFgryDCAWroHXwGoaTStLRQPmCs7GUwilqEnEqB6cNYloHhDcig0LQ0PuTUimJIQ6yxNzglwjA0TWCIAzEsBdM+Aw6IIQDc3YfSWZQnVwAAAABJRU5ErkJggg==)
. Так как
![](data:image/png;base64,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)
, то
![](data:image/png;base64,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)
- нормальная подгруппа в
![](data:image/png;base64,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)
. Из того, что
![](data:image/png;base64,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)
следует, что
![](data:image/png;base64,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)
- нормальная силовская
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEISURBVDjLY2hsbGQgBzNQXWMoAwMzAxivYlrFwMDEwPCfEa9GIGDMywuVMWZgvANk/5F1yymOMGJaZBzb4I1XY3WWi7EsA+NrWY+cQhA/z0O2iIHB+E5sfb0kTo3l5Wm87jKMexiMo+bDxGojDf0YjKMX4PVjfaSxL7LpHUCD3GQY9hpHN/jg1RhlzLAQaNtCEPs/0K85brIlDAyyrz2KGwzwaow2ZpjPYBSxCBSa1ZGmvrImJstlZT1XpHV08ODV2FDsYSDHwPASFJogf4JslPXIKyIpHjs60ng8ZGVXeuTVGxKtERT5oLg0ZDDcE1peL02Uxvr6WEkjBoZbYOdCnUyftDr4NAIANPdQAloOMQ4AAAAASUVORK5CYII=)
-подгруппа в
![](data:image/png;base64,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)
. Полученное противоречие показывает, что
![](data:image/png;base64,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)
не является нильпотентной подгруппой.
Так как
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEcSURBVDjLY2hsbGSgFDPQzBAgYIJiRmTxVQhxIF7FhNOQ+jwPQ1kGhleMDAz/ZN1ySpDloowZ5gMN+AfEfxmMo+YT9A5Qw0IGBuO7sfX1ksjiOW6yxcaxDd4EvVNfHytpYmIyw5iB4Y5xZL0vTLyjI43HzditNq2jg4egIQ3Rxj7G0Q0+eR6yRQxGUYuQvWrslpdCVMDmubmFgbwBCR/Zmy5Z1UYQceMUj7x6Q4KGgJzs4RGdDGfLMuwGBTAur+CMHY/IejtkrzHIuO/JynKxw+YVrIagOxkUyKAAlpU12Y7NKyiGgBJWWlooH9DJdaFpaXzIiqKNGRYwyHrsxuYVFEMaYo29wYkIhGXddyFrAHnR1CMvmf55Z+gaAgA7AZreUdHWggAAAABJRU5ErkJggg==)
является максимальной подгруппой в
![](data:image/png;base64,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)
, то по условию все 2-максимальные подгруппы группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEcSURBVDjLY2hsbGSgFDPQzBAgYIJiRmTxVQhxIF7FhNOQ+jwPQ1kGhleMDAz/ZN1ySpDloowZ5gMN+AfEfxmMo+YT9A5Qw0IGBuO7sfX1ksjiOW6yxcaxDd4EvVNfHytpYmIyw5iB4Y5xZL0vTLyjI43HzditNq2jg4egIQ3Rxj7G0Q0+eR6yRQxGUYuQvWrslpdCVMDmubmFgbwBCR/Zmy5Z1UYQceMUj7x6Q4KGgJzs4RGdDGfLMuwGBTAur+CMHY/IejtkrzHIuO/JynKxw+YVrIagOxkUyKAAlpU12Y7NKyiGgBJWWlooH9DJdaFpaXzIiqKNGRYwyHrsxuYVFEMaYo29wYkIhGXddyFrAHnR1CMvmf55Z+gaAgA7AZreUdHWggAAAABJRU5ErkJggg==)
перестановочны с каждой максимальной подгруппой группы
![](data:image/png;base64,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)
. Ввиду следствия , группа
![](data:image/png;base64,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)
имеет вид
![](data:image/png;base64,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)
, где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADdSURBVDjLY2hsbGQgBzNQReMqBgYmBrx4FRNWjVHGDAuBCv5C8T8GBsZ/KHzj6AUYGjs60ng85ExmxtbXS4L4OW6yJQyyHrvTOjp4QPw8D9ki49gGbwyN9Xkehh6xDbZwQ2QY9sh65BXB5SMjDWGG4gyc6iwXI1kG2ZseefWGJIUq2JkMxneQbSCoEeZM5IAgSmN5eayUMQPDXeSAIEpjfaSxLyFnYmgEAsYoI4ZFhJyJohGUaoChaSzLwPDGMLLWDzmV4NQIChB3WYZdSKnkD4Os+y5Y5NMukdNFIwBxfUo7Pgx8DAAAAABJRU5ErkJggg==)
- группа простого порядка
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
- циклическая
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD+SURBVDjLY2hsbGQgBzNQXWMoAwMzAxj/Z1zFwMAEZDPi1QhSUF4eKm3MwHgHyP4j65ZTHGHEtMg4tsEbr8bqLBdjWQbG17IeWUUgfo6bbDEDg/Gd2Pp6SZway8vTeN1lGPcwGEfNh4nVRxr7MhhHL8DrR7AiJNM7gAa5yTDsNY5u8MGrMcqYYSHQtoUwvwKdWcLAIPvaI6/eEK/GaGOGBQxGEYtAoQmyXdbEZLmsrOeKtI4OHrwaG4o9DOQYGF6CQhPkT5CNsh55RSTFY0dHGo+HrOxKbM7EqREU+Xl5oTJGDEZ7QsvrpYnSWF8fK2nEwHAL7Fyok+mTVgefRgAoBE5onQ0lPAAAAABJRU5ErkJggg==)
-подгруппа.
Так как
![](data:image/png;base64,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)
и факторгруппа
![](data:image/png;base64,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)
изоморфна подгруппе из
![](data:image/png;base64,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)
, то
![](data:image/png;base64,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)
больше
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD+SURBVDjLY2hsbGQgBzNQXWMoAwMzAxj/Z1zFwMAEZDPi1QhSkJcXKmPMwHgHyP4j65ZTHGHEtMg4tsEbr8bqLBdjWQbG17IeWUUgfo6bbDEDg/Gd2Pp6SZway8vTeN1lGPcwGEfNh4nVRxr7MhhHL8DrR7AiJNM7gAa5yTDsNY5u8MGrMcqYYSHQtoUwvwKdWcLAIPvaI6/eEK/GaGOGBQxGEYtAoVkfaeora2KyXFbWc0VaRwcPfqfmeRjKMTC8BIUmyJ8gG2U98opIiseOjjQeD1nZldiciVMjKPJBcWnEYLQntLxemiiN9fWxkkYMDLfAzoU6mT5pdfBpBADviU5UXyUMIQAAAABJRU5ErkJggg==)
.
Если
![](data:image/png;base64,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)
- нильпотентная группа, то
![](data:image/png;base64,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)
и поэтому согласно теореме Бернсайда , группа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADtSURBVDjLY2hsbGQgBzNQXSMQMEEx4yooTVBjeXmotDEDwx2g4r+ybjnFEUYMi4yjG3zwaqzOcjGSZWB8LeuRVwTi57jJFjMwGN+Jra+XxKmxvDyN112GYQ+DcfQCmFh9pLEvMh+rRrAiJNNhBqE7E0NjlDHDQgbjqIXQwGEEOrOEgUH2tUdevSFejdHGDAsYjCIWgUITZLusiclyWVnPFWkdHTz4nZrnYSjLwPAKFJoMxpELQDbCAonoeOzoSOPxkJVdic2ZODWCnAqKSyMGoz2x5eVSRGmsr4+VBEb+bbBzwU6Omk+ftDr4NAIA8sFOPQSqDIcAAAAASUVORK5CYII=)
-нильпотентна. Но тогда
![](data:image/png;base64,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)
. Полученное противоречие показывает, что
![](data:image/png;base64,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)
является ненильпотентной группой. Так как
![](data:image/png;base64,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)
- нормальная подгруппа в
![](data:image/png;base64,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)
, то ввиду следствия , подгруппа
![](data:image/png;base64,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)
имеет вид
![](data:image/png;base64,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)
, где
![](data:image/png;base64,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)
- циклическая
![](data:image/png;base64,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)
-подгруппа, и, следовательно,
![](data:image/png;base64,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)
. Полученное противоречие показывает, что в группе
![](data:image/png;base64,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)
существует нормальная силовская подгруппа.
Пусть, например, такой является силовская
![](data:image/png;base64,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)
-подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADoSURBVDjLY2hsbGQgBzNQVSMQMAIxEzaMV2NDrLE3UNFfIP4PpcGYkcH4bmh5uTRep9bneRjKMjC8MY5t8AbxOzrSeDxkGXYzyHjsSevo4MGtMdLYl4HB+E5sfb0kTCzHTbYEKHYXJIZTY5QRwyIG4+gFMD7QzYwRIDFZj904bSwvj5UyZmC4axhZ6wcNFOYssG0Mf2FOx+NMxn9IAfMH6MTbyM7G7Uyok4iOx/r6WEmQM2U98opISgDVWS5GcgxyNzyKGwyI1ggKCHDIGUUsYmBYxUSURmiEv4IHhqz7LpL8ODC5gxgMAKHGRmhcQLDfAAAAAElFTkSuQmCC)
группы
![](data:image/png;base64,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)
. Пусть
![](data:image/png;base64,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)
. Ясно, что
![](data:image/png;base64,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)
.