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In mathematical finite group theory, the Thompson order formula, introduced by John Griggs Thompson , gives a formula for the order of a finite group in terms of the centralizers of involutions, extending the results of . ==Statement== If a finite group ''G'' has exactly two conjugacy classes of involutions with representatives ''t'' and ''z'', then the Thompson order formula states :|G| = |C''G''(''z'')|''a''(''t'') + |C''G''(''t'')|''a''(''z'') Here ''a''(''x'') is the number of pairs (''u'',''v'') with ''u'' conjugate to ''t'', ''v'' conjugate to ''z'', and ''x'' in the subgroup generated by ''uv''. gives the following more complicated version of the Thompson order formula for the case when ''G'' has more than two conjugacy classes of involution. : where ''t'' and ''z'' are non-conjugate involutions, the sum is over a set of representatives ''x'' for the conjugacy classes of involutions, and ''a''(''x'') is the number of ordered pairs of involutions ''u'',''v'' such that ''u'' is conjugate to ''t'', ''v'' is conjugate to ''z'', and ''x'' is the involution in the subgroup generated by ''tz''. 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「Thompson order formula」の詳細全文を読む スポンサード リンク
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