On the cohomology of split extensions of finite groups
Title: On the cohomology of split extensions of finite groups
Author: Stephen F. Siegel
This paper will appear in the Trans. Amer. Math. Soc.
Abstract: Let $G=H\rtimes Q$ be a split extension of finite groups,
and consider the Lyndon-Hochschild-Serre spectral sequence of the
extension with coefficients in a field $k$. The $E_{2}$-page is
isomorphic to $H^*(Q,H^*(H,k))$ and it converges to $H^*(G,k)$ modulo
a certain filtration. A theorem of Charlap and Vasquez gives an
explicit description of the differentials $d_2$ in this case. We
generalize this to give an explicit description of all the $d_r$
($r\geq 2$). The generalization is obtained by associating to the
group extension a certain twisting cochain. The twisting cochain not
only determines the differentials, but also allows one to construct an
explicit $kG$-projective resolution of $k$.
----------------------------------------------------------------------------
This article is available in the following formats:
* LaTeX2e Source
* DVI file
* Postscript file
Related Items:
* Other papers by the same author
Author address:
Stephen F. Siegel
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
708-491-5594