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In mathematics, especially in the fields of group cohomology, homological algebra and number theory the Lyndon spectral sequence or Hochschild–Serre spectral sequence is a spectral sequence relating the group cohomology of a normal subgroup ''N'' and the quotient group ''G''/''N'' to the cohomology of the total group ''G''. ==Statement== The precise statement is as follows: Let ''G'' be a finite group, ''N'' be a normal subgroup. The latter ensures that the quotient ''G''/''N'' is a group, as well. Finally, let ''A'' be a ''G''-module. Then there is a spectral sequence: :''H'' ''p''(''G''/''N'', ''H'' ''q''(''N'', ''A'')) ⇒ ''H'' ''p+q''(''G, ''A''). The same statement holds if ''G'' is a profinite group and ''N'' is a ''closed'' normal subgroup. 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「Lyndon–Hochschild–Serre spectral sequence」の詳細全文を読む スポンサード リンク
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