On the Cohomology of Split Extensions of Finite Groups
نویسنده
چکیده
Let G = HoQ be a split extension of nite groups. A theorem of Charlap and Vasquez gives an explicit description of the di erentials d2 in the Lyndon-Hochschild-Serre spectral sequence of the extension with coe cients in a eld k. We generalize this to give an explicit description of all the dr (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 di erentials, but also allows one to construct an explicit kG-projective resolution of k.
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