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In mathematics, a 3-step group is a special sort of group of Fitting length at most 3, that is used in the classification of CN groups and in the Feit–Thompson theorem. The definition of a 3-step group in these two cases is slightly different. ==CN groups== In the theory of CN groups, a 3-step group (for some prime ''p'') is a group such that: *''G'' = O''p'',''p''′,''p''(''G'') * O''p'',''p''′(''G'') is a Frobenius group with kernel O''p''(''G'') *''G''/O''p''(''G'') is a Frobenius group with kernel O''p'',''p''′(''G'')/O''p''(''G'') Any 3-step group is a solvable CN-group, and conversely any solvable CN-group is either nilpotent, or a Frobenius group, or a 3-step group. Example: the symmetric group ''S''4 is a 3-step group for the prime ''p''=2. 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「3-step group」の詳細全文を読む スポンサード リンク
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