On the cohomology of split extensions of finite groups

Abstract. Let G=H:Q be a split extension of finite groups. A theorem of Charlap and Vasquez gives an explicit description of the differentials d₂ in the Lyndon-Hochschild-Serre spectral sequence of the extension with coefficients in a field k. We generalize this to give an explicit description of all the d_r (r 2) in this case. The generalization is obtained by associating to the group extension a new twisting cochain, which takes values in the kG-endomorphism algebra of the minimal kH-projective resolution induced from H to G. This twisting cochain not only determines the differentials, but also allows one to construct an explicit kG-projective resolution of k.

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