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In mathematics, or more specifically group theory, the omega and agemo subgroups described the so-called "power structure" of a finite ''p''-group. They were introduced in where they were used to describe a class of finite ''p''-groups whose structure was sufficiently similar to that of finite abelian ''p''-groups, the so-called, regular p-groups. The relationship between power and commutator structure forms a central theme in the modern study of ''p''-groups, as exemplified in the work on uniformly powerful p-groups. The word "agemo" is just "omega" spelled backwards, and the agemo subgroup is denoted by an upside-down omega. == Definition == The omega subgroups are the series of subgroups of a finite p-group, ''G'', indexed by the natural numbers: : The agemo subgroups are the series of subgroups: : When ''i'' = 1 and ''p'' is odd, then ''i'' is normally omitted from the definition. When ''p'' is even, an omitted ''i'' may mean either ''i'' = 1 or ''i'' = 2 depending on local convention. In this article, we use the convention that an omitted ''i'' always indicates ''i'' = 1. 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「omega and agemo subgroup」の詳細全文を読む スポンサード リンク
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