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Focal subgroup theorem : ウィキペディア英語版 | Focal subgroup theorem In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in and is the "first major application of the transfer" according to . The focal subgroup theorem relates the ideas of transfer and fusion such as described in . Various applications of these ideas include local criteria for ''p''-nilpotence and various non-simplicity criterion focussing on showing that a finite group has a normal subgroup of index ''p''. == Background ==
The focal subgroup theorem relates several lines of investigation in finite group theory: normal subgroups of index a power of ''p'', the transfer homomorphism, and fusion of elements.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Focal subgroup theorem」の詳細全文を読む
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