![](data:image/png;base64,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)
является нормальной подгруппой в
![](data:image/png;base64,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)
и поэтому
![](data:image/png;base64,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)
- нормальная подгруппа в группе
![](data:image/png;base64,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)
. Это означает, что
![](data:image/png;base64,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)
- группа типа (5).
II.
![](data:image/png;base64,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)
.
Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGQgBzNQVSMQMAIxMyYOZcarsSHW2Buo8C8Q/4fSf0CYkcHobmh5uTRep9bneRjKMjC+MY5t8AbxOzrSeDxkGXYzyHjsSevo4MGtMdLYl4HB+E5sfb0kTCzHTbYEKHYXJIZTY5QRwyIG4+gFMD7QzYwRIDFZj904bSwvj5UyYmC4axhZ6wcLmCywbQx/YE7H40zGf7BAgWCjW8jOxu1MqJOIjsf6+lhJY6AzZT3yikhKANVZLkZyDHI3PIobDIjSCEst4JAziljEwLCKiSiNDcUeBnIMDC/hgSHrvoskPw5M7iAGAwAXgkU/4D5+5wAAAABJRU5ErkJggg==)
- некоторая силовская
![](data:image/png;base64,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)
-подгруппа группы
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
- некоторая силовская
![](data:image/png;base64,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)
-подгруппа группы
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
- некоторая силовская
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAOCAYAAAAbvf3sAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVCjPY2hsbGQgBTNQpCGUgYGZAYz/M4L4qxgYmBgYVjFh1VBfHytpzMBwm5GB4Z+sW05xeVoon4cMwx4G4+gFOG0oL0/jBSkyjc6L8JSVXWFiIrtM1iOrCKeG6iwXI1kGo1Nubsa1HsUNBgT9kOMmW8IgK3vT1CMvmShPRxkxLGKQ9did1tHBQ1BDeXmslBED413j2AZvooK1PtLYl4HB+E5sfb0kURryXGStgEEYSNuYpokGAHcp8CGxwxfAAAAAAElFTkSuQmCC)
-подгруппа группы
![](data:image/png;base64,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)
, где
![](data:image/png;base64,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)
- различные простые делители порядка группы
![](data:image/png;base64,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)
. Пусть
![](data:image/png;base64,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)
- произвольная нормальная максимальная подгруппа группы
![](data:image/png;base64,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)
. Так как
![](data:image/png;base64,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)
- разрешимая группа, то индекс подгруппы
![](data:image/png;base64,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)
в группе
![](data:image/png;base64,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)
равен некоторому простому числу. Пусть, например, индекс
![](data:image/png;base64,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)
равен
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADtSURBVDjLY2hsbGQgBzNQXSMQMEEx4yooTVBjeXmotDEDwx2g4r+ybjnFEUYMi4yjG3zwaqzOcjGSZWB8LeuRVwTi57jJFjMwGN+Jra+XxKmxvDyN112GYQ+DcfQCmFh9pLEvMh+rRrAiJNNhBqE7E0NjlDHDQgbjqIXQwGEEOrOEgUH2tUdevSFejdHGDAsYjCIWgUITZLusiclyWVnPFWkdHTz4nZrnYSjLwPAKFJoMxpELQDbCAonoeOzoSOPxkJVdic2ZODWCnAqKSyMGoz2x5eVSRGmsr4+VBEb+bbBzwU6Omk+ftDr4NAIA8sFOPQSqDIcAAAAASUVORK5CYII=)
. Ввиду следствия ,
![](data:image/png;base64,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)
- либо нильпотентная подгруппа, либо ненильпотентная группа порядка
![](data:image/png;base64,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)
.
1. Предположим, что
![](data:image/png;base64,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)
- нильпотентная подгруппа. Пусть
![](data:image/png;base64,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)
- силовская
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD/SURBVDjLY2hsbGQgBzNQTSMQMAIxMxQzrmJgYIKwQ5nxaqzP8zCUZWB4BVT8zzCy1i/SmGEBkP2HkcHobmx5uRRep5aXx0oZMciekpNjuG4c2+Dd0ZHG4yHDsEfWLacYr8b6SGNfBlnjE5F59aoQg9J4wRo98orwaowyZlgIsgnGr85yMZJjkLvhUdxggNuP9bGSRgxGu2Pr6yVBfFDgRBgxLWIwjpqPN3BApsvKuq8KTUvjB4VmpDHTQgYGo1swg3BqzHGTLQFq+AsKSTBGswmrRnAgyMqu9MirNyQ6AYD8AnSmMcSZ5XxEawSG5Hy482Tdd6V1dPDQJ60OXo0Awy9L334zYzoAAAAASUVORK5CYII=)
-подгруппа группы
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
- силовская
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAOCAYAAAAbvf3sAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACtSURBVCjPY2hsbGQgBTNQpAEImKCYEcRfBWavYsKqob4+VtKYgeE2IwPDP1m3nOK0tFA+DxmGPQzGUQtx2tDRkcYDUmQanRfhKSu7wsREdpmsR14RTg3VWS5GsgxGp9zcjGs98uoNCfohx022mEFW9qapR14yUZ6OMmJYxCDrsTuto4OHoAaop+8aRzf4EBWsDdHGPgwMxndi6+slidKQ5yJrxWAcHUjbmKaJBgCrGe7p2jBFywAAAABJRU5ErkJggg==)
-подгруппа группы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAARCAYAAADdRIy+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAF2SURBVDjLzZSxTgJBEEDnoBVrMSydvdxAY32um4gmFBSwuQpzMYQsCafZQvGOjvgJWgiUfIP+gN8gP2D4BA3uCBeV3CGFUYvJXWZn3+672Vvo9XrwkwG/AhwDpAAgDVBNJ04EsOY1FDNrJbCOcGcKXwFw4gZBNg7WrRWOzWNm3l+YaHa+VQ5qeATApkIFheWxi6ZjM4CpWfBpecFEoEQYWDFArb3MAeZvCMiE6qz1DbV2tznnbQSYoAzLn1UVxxPOsUu66IaHawFJt+S6jWUgqZaEarQ4O4vTTQRKxKAWqB2Rg3vGW36kKlBcqlBtmfwDoBysdWxIF1FeLbo9BKwPI1Xhh7vzhljTON1YIOlGxdQYAkaqlFulGwsk3ajYTPaB2Y/Forj2+v0N2mndhlGS7hfgjLRUNYf5/duq521SLpRYNmfxmVTp79GeU3w/Lvz0HGCcWglUDtszOwjngW1P60ygnSw6vr3Qr3yMm0BZ+bvL4V8B3wBzZNLr6A0gWQAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
- силовская
![](data:image/png;base64,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)
-подгруппа группы
![](data:image/png;base64,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)
. Тогда
![](data:image/png;base64,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)
. Так как
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
, то
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
- нормальные подгруппы в группе
![](data:image/png;base64,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)
. Из того, что индекс подгруппы
![](data:image/png;base64,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)
равен
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD+SURBVDjLY2hsbGQgBzNQXWMoAwMzAxj/Z1zFwMAEZDPi1QhSUF4eKm3MwHgHyP4j65ZTHGHEtMg4tsEbr8bqLBdjWQbG17IeWUUgfo6bbDEDg/Gd2Pp6SZway8vTeN1lGPcwGEfNh4nVRxr7MhhHL8DrR7AiJNM7gAa5yTDsNY5u8MGrMcqYYSHQtoUwvwKdWcLAIPvaI6/eEK/GaGOGBQxGEYtAoQmyXdbEZLmsrOeKtI4OHrwaG4o9DOQYGF6CQhPkT5CNsh55RSTFY0dHGo+HrOxKbM7EqREU+Xl5oTJGDEZ7QsvrpYnSWF8fK2nEwHAL7Fyok+mTVgefRgAoBE5onQ0lPAAAAABJRU5ErkJggg==)
, следует, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAXCAYAAAAV1F8QAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGpSURBVEjH7ZW/TsJAHMd/MKOzKNd3gB+O4kKOS8CRmLbpBHYgzS2YdABzZevgCxAHxJEH0MQ/z+GgvIDhFTTelRIraY0WcGL4Lde7++S+v+/3VxgMBvAfBVvQWkETgCyElXgQIANf+zKpQAbCSB5+B8CpJUQ+bo9Dybm8/0PtQ8urp5ZO6HgCQGaMi+Lyt16nWiIAMyDswfb9XGrpfN/OMQIPcSDXtfbLhNwqEJpeY6UeCc6KyFgfAabRy1QvTERhmngmZX1NkvXXIE6xXeX8iBXgkVCnG5VTgY0S3ACa1yu5LpANWZ97fC8KCvqC5qUQVn75palASjami0rovjGgMXZde0fBVePnJvmbbLEgh9LTxSXSwl0o0CdW1oYLU8xlM8apA6sa7brNA9RqV03b3lVrnomNRU5UiKV8qNwm5ZQZmmR/CHImEeRZWJ+HNAjqi3qVkvGQ8db3EIeFxigO0tH1Y0en9WqnV9rYrAsU0LRnrcyGFOlFNMxrBQmdVVQvo0psBKRT2lb9NRlrLY+mtUHC0XQnzfIWN2TXBgrMQmr3SUN2+ytPXZ/nf1iojihRagAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
- силовские подгруппы группы
![](data:image/png;base64,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)
и поэтому
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. Понятно, что для некоторого
![](data:image/png;base64,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)
имеет место
![](data:image/png;base64,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)
и поэтому, не теряя общности, мы можем полагать, что
![](data:image/png;base64,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)
. Следовательно,
![](data:image/png;base64,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)
. Ясно, что
![](data:image/png;base64,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)
не является нормальной подгруппой в группе
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD5SURBVDjLY2hsbGSgFDPQ3BAgYELCjFAxRqIMASmsznIxkmVgeA1k/wVjWY/daeVpUm7GbrVpHR08eA0pL0/j9ZBh2MPAIPvKI6/eECZen+dhCDbUOHoBXpfADQDZimYbCOe4yRYbRzf44DUEqKgE6ILXyC5AxvWRHnbY5OCMjo40HrArjKMWoocPWgAz4TSkvj5W0piB4a6sW04xsoKGWGNvaOD+B+J/DAzGt2Pr6yUJGVKC4Q2oHLZAxfSOLMNuBhmPPWnl5byoYWHsCwyrN7jCCtVGSDS+AoULchhEGTEswhVjWNMJ1Om34YkMio1jG7wHLu8MPUMA9sSNgymq2SEAAAAASUVORK5CYII=)
.
Если подгруппы
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
нильпотентны, то
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
, и поэтому
![](data:image/png;base64,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)
- нормальная подгруппа в группе
![](data:image/png;base64,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)
. Значит, подгруппы
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
не могут быть обе нильпотентными подгруппами. Следовательно, возможны следующие случаи.
а)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAUCAYAAACTQC2+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGHSURBVEjH5VU7bsJAEB1SI3oU7yFgDpAGoZUIpQtjuXVhWS5IJAqKxZ2LHAJyDeAgEXAB8BWw4rW9/qy9gIhIg6UpVh6/N/PmzRp834f/CHgOovhpxfEihxKknt+6ichEWMbJURbnNMhp4Mz7MoFt6x1KYF3kQUSG7qdMpmx1grACQtd2ELRzco1uxJkDuUPCAc9oLUbiu4WFI06GBhtfJQoCu0012BDqTXMAE9/jrkLqsR4/pyTkJM61IktFKYnmzqBPgPwIkKJ63FuMddP3EJYLuYsoAdXoVrftDh8uM3DMJRLACRDggZOq1CjL3kiUJxbD5UY4iu4Ys7oIcACcrNRq1Lu9KpsczKO9BGjofjTZfNKHbyHxRaJENqntClHa0Z5bWCbJXBiVXVgjyndCg23THpTDo2Sa7RWKJU3nVrV6I1Hm/3wuKkdJS13MEc3lQ+463r1hOG9NV9PNV9DFymKQ2Ux/jTXbZY4MyxImZkLz689EqcS4467KHHisSKgw0pP8jx4Rvy3SwUEGegPYAAAAAElFTkSuQmCC)
и
![](data:image/png;base64,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)
- группы Шмидта.
Так как
![](data:image/png;base64,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)
, то ввиду следствия ,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADvSURBVDjLY2hsbGQgBzNQVSMQMAIxMyYOZcarsSHW2Buo8C8Q/4fSf0CYkcHobmh5uTRep9bneRjKMjC+MY5t8AbxOzrSeDxkGXYzyHjsSevo4MGtMdLYl4HB+E5sfb0kTCzHTbYEKHYXJIZTY5QRwyIG4+gFMD7QzYwRIDFZj904bSwvj5UyYmC4axhZ6wcLmCywbQx/YE7H40zGf7BAgWCjW8jOxu1MqJOIjsf6+lhJY6AzZT3yikhKANVZLkZyDHI3PIobDIjSCEst4JAziljEwLCKiSiNDcUeBnIMDC/hgSHrvoskPw5M7iAGAwAXgkU/4D5+5wAAAABJRU5ErkJggg==)
- подгруппа простого порядка
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAARCAYAAADtyJ2fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADpSURBVDjLY2hsbGQgBzNQVSMQMEExIxSD+Xg11ud5GMoyMLwCKvxnHFnvG23MsADI/svAYHw3trxcCq+N9fWxkkYMsqfk5BhuGMc2eHd0pPF4yDDskXXLKcavMdLYl0HW+GRkXr0qiA/X6JFXhFdjlDHDQuPoBh8YvzrLxUiOQe6GR169IW4/gp1ptDu2vl4SGlCMIIMYjKMX4A0ckOmysh6rQtPS+EAhCdbEYHwbZhBOjTlussWQUIRiNJuwagQHgqzsSmS/EEwAIL8AnWkMcmZaeTkv0RoREQ3Esp670jo6eOiXVgenRgAfW0uHZv/1bAAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
- циклическая подгруппа, которая не является нормальной в группе
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAUCAYAAACTQC2+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAG5SURBVEjH5VVNTsJAFP6KW5W1kccZhDmAG1MnIbgjsSVsG9IQFqDpgpjCjsRDoC45guBBVDyA2iOAONM6cSytEAluWLykP6/ve9/3vjdFr9fDfwS2A2gIZADsJISxWv7cWAnIZhgYwIeoKwJTGQbo/cTtMD1vLhIcp5LlhJHKEzEjs34ZbyqVqgC7BfGR0+/vyvsqww1yfKzuJYhr0oUszmrdkvquW2Ml2SSz/PJSIM9z9ngOY+LNlnrmW6wMUMCbfkF22whB6I23u0eJTWpNpQJ13JMigR5l0TBJFK6bJORgk5rvH0TvjUBv5E9AYbc586HiOFk53CurcBZqz92wsF3EnQJNUeNBlz0RSMkmC38POP+qJPL92gEDXsCqN+lqLLJdKls8/CYvEBCQ2WjH30mDnEdsn+Nsk2WL0f4BFDGaCKAL3cJyl6I5Yqa7cAEIXzthCn2jPZgbadZ3ObXUXqkltVjmNm71RCDpf23ppmrwv+zZ4MccmT3YyFkn2O9blnscP5rkNTDMrA0kC3le5VBo9hwxokCXUJiJEbOv1waKJC4+SVdJB+aBV11y0Ol9kpG25H+0ifgELBDA28o/U2oAAAAASUVORK5CYII=)
, но максимальная подгруппа
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAUCAYAAABroNZJAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFxSURBVDjLzZTNTsJAFIVPcYu6JvayZikdH8HAkIAJiyb8hO0sCGFBSbowZsquiS/gDmXJI2B9EFEeQHkFjXaKFRik/m1ocpN20n6959wzg8FggP8Wdh8SXkZYe8sap34FGQMpWWeV8OOXuFJWbQS8GT+CuMI+KJpGACpOhO+n1ZqUrQwDHqnQ6X8LURJqFkag0icgrk6BHJg80Nc3IAsJNOeOd6y/GEL6AJu1pMxshfi+SHMTAVjz+quWGww3IH6b2MmH7hlreuUNn1yxXzBxR7zbS/REdnmeQPe8K/O6Txf1/Nk2mWsQz+HHBMxZXVZWAeftU0Yw5sTbURd2lJn1Ueu6h4ZZDGwhDlXAFgA8gzWGK5IfwlE7WyHK3BJhsgxZ9kmX4DVZORGi2ndENVcVTk6PefycCFGAOOrhpnlFFPPFvnFd++gky6/UeBMhkbGscanu25x6q/sGsKZxyNSkVPzVT/90FChjLWCqe7U7h9I7z3/Pfm2UiYwAAAAASUVORK5CYII=)
группы
![](data:image/png;base64,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)
нормальна в
![](data:image/png;base64,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)
. Аналогично видим, что
![](data:image/png;base64,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)
- подгруппа простого порядка
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAOCAYAAAAbvf3sAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACWSURBVCjPY2hsbGQgBTPQT0N9faykMQPDXQYGhv+ybjnFHR1pPB4yDHsYjKMW4rQBpsg0Oi/CQ1Z2pYmJ7AqQZpwa6vM8DGUZjE65uRnXeuTVGxL0Q46bbDGDrOxNY7e8FKI8HWXMsJBBxmNPWkcHD9GeNo5u8CEqlBqijX0YGIzvxtbXSxKlIc9F1orBODpwEMU0sRgAF3L1eF2ssogAAAAASUVORK5CYII=)
и
![](data:image/png;base64,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)
- нормальная подгруппа в
![](data:image/png;base64,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)
. Отсюда следует, что
![](data:image/png;base64,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)
- нормальная подгруппа в
![](data:image/png;base64,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)
, и поэтому
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD5SURBVDjLY2hsbGSgFDPQ3BAgYELCjFAxRqIMASmsznIxkmVgeA1k/wVjWY/daeVpUm7GbrVpHR08eA0pL0/j9ZBh2MPAIPvKI6/eECZen+dhCDbUOHoBXpfADQDZimYbCOe4yRYbRzf44DUEqKgE6ILXyC5AxvWRHnbY5OCMjo40HrArjKMWoocPWgAz4TSkvj5W0piB4a6sW04xsoKGWGNvaOD+B+J/DAzGt2Pr6yUJGVKC4Q2oHLZAxfSOLMNuBhmPPWnl5byoYWHsCwyrN7jCCtVGSDS+AoULchhEGTEswhVjWNMJ1Om34YkMio1jG7wHLu8MPUMA9sSNgymq2SEAAAAASUVORK5CYII=)
является группой типа (7).
б) Одна из подгрупп
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
является нильпотентной, а другая - группой Шмидта.
Пусть например,
![](data:image/png;base64,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)
- группа Шмидта и
![](data:image/png;base64,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)
- нильпотентная подгруппа. Из следствия следует, что
![](data:image/png;base64,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)
- группа простого порядка
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
- циклическая группа и максимальная подгруппа
![](data:image/png;base64,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)
из
![](data:image/png;base64,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)
нормальна в
![](data:image/png;base64,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)
. Так как
![](data:image/png;base64,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)
- нильпотентная группа, то
![](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,iVBORw0KGgoAAAANSUhEUgAAABoAAAAUCAYAAACTQC2+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGSSURBVEjH5VUxbsIwFP0wI3bU+BDwD9AFpZZouyE1QVkzIJSBVmJAlcmWoXeg6dgjFDhIBb0AcAWq2klMncQuqBVdGN5g8fPe/8/vGwjDEP4DcB5CrwBV0MBEoqmvHCXkIkwrAJ+8ngN2AhUgm3Z/3Mp9zAt8v1unBGayToDYg4eimHFULhYDoTM/imri3EN4BovO5VkQDWwiCHfoTTryu4mHHdEkOuzmoFAU+TVqwZzQYLgn6OE1ANnSgDXFORUhG3kuNak0ZRQa99stAuRdknx3jyuPsUb6O2zVRn4llJBa9qLr+3VxuY9O8zbxPiN2W/AiRU1uqLZrhfaFyuVyi9ZyOsa8BgJ8ALqx2Y3ytAdtK4IFtJkQ2YP7UoS5xXeGafW2FcbOCaUTrUSEi7ukS2FJSO6EbcFCtwcqAkqG2V6hXFIHq7FJJCck8p9bOkOiJJK9Uu8R3elJ3joxveP0L3VP09FP0I+dcZLRqHvBPVtmidyqFiZhwt7Tn4VSi3EpUpUlcJ2zkFy96YJ0Jv9Hp8AXX53DNh/9uhAAAAAASUVORK5CYII=)
- нормальная подгруппа в группе
![](data:image/png;base64,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)
. Значит, ввиду леммы ,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAUCAYAAACTQC2+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGSSURBVEjH5VUxbsIwFP0wI3bU+BDwD9AFpZZouyE1QVkzIJSBVmJAlcmWoXeg6dgjFDhIBb0AcAWq2klMncQuqBVdGN5g8fPe/8/vGwjDEP4DcB5CrwBV0MBEoqmvHCXkIkwrAJ+8ngN2AhUgm3Z/3Mp9zAt8v1unBGayToDYg4eimHFULhYDoTM/imri3EN4BovO5VkQDWwiCHfoTTryu4mHHdEkOuzmoFAU+TVqwZzQYLgn6OE1ANnSgDXFORUhG3kuNak0ZRQa99stAuRdknx3jyuPsUb6O2zVRn4llJBa9qLr+3VxuY9O8zbxPiN2W/AiRU1uqLZrhfaFyuVyi9ZyOsa8BgJ8ALqx2Y3ytAdtK4IFtJkQ2YP7UoS5xXeGafW2FcbOCaUTrUSEi7ukS2FJSO6EbcFCtwcqAkqG2V6hXFIHq7FJJCck8p9bOkOiJJK9Uu8R3elJ3joxveP0L3VP09FP0I+dcZLRqHvBPVtmidyqFiZhwt7Tn4VSi3EpUpUlcJ2zkFy96YJ0Jv9Hp8AXX53DNh/9uhAAAAAASUVORK5CYII=)
- нормальная максимальная подгруппа в группе
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADmSURBVDjLY2hsbGSgFDPQ3BAgYETGMDGiDAEprM5yMZJlYHgNZP8DY1mP3Wn1aZJuxm61aR0dPHgNKS9P4/WQYdjDwCD72iOv3hAmXp/nYQg21DhqIV6XwA0A2YpmGwjnuMkWG0c3+OA1BKQI6II3yC5AxvWRHnbY5OCMjo40HrArsDkXSwBjNaS+PlbSmIHhrqxbTjGygoZoYx9o4P6H0MZ3YuvrJUkyBFmOwTh6Ad50AvaOLMNuBhmPPWnl5byYrsEdVqg2IkUjchhEGTEswhVjWNMJ1Ol34IkMirFFLf3yztAzBADnvY8M78csLQAAAABJRU5ErkJggg==)
и поэтому
![](data:image/png;base64,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)
. Следовательно,
![](data:image/png;base64,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)
- группа простого порядка
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAOCAYAAAAbvf3sAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACWSURBVCjPY2hsbGQgBTPQT0N9faykMQPDXQYGhv+ybjnFHR1pPB4yDHsYjKMW4rQBpsg0Oi/CQ1Z2pYmJ7AqQZpwa6vM8DGUZjE65uRnXeuTVGxL0Q46bbDGDrOxNY7e8FKI8HWXMsJBBxmNPWkcHD9GeNo5u8CEqlBqijX0YGIzvxtbXSxKlIc9FUpbBOFJjEMU0sRgA4Wn1LBLFDWsAAAAASUVORK5CYII=)
.