The Lyndon–Hochschild–Serre spectral sequence is a tool in algebraic topology and homological algebra that arises in the context of group cohomology and the study of group extensions. It provides a method for computing the cohomology of a group \( G \) by relating it to the cohomology of a normal subgroup \( N \) and the quotient group \( G/N \).
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For a normal subgroup , quotient , and a -module , the Lyndon–Hochschild–Serre spectral sequence has