On the cohomology of split extensions of elementary abelian $2$-groups
and Totaro's example

Author: Stephen F. Siegel

To appear in Journal of Pure and Applied Algebra

Abstract: In a previous paper we dervied an expression for the
differentials in the Lyndon-Hochshild-Serre spectral sequence of a
split extension $G=H\rtimes Q$ of finite groups with coefficients in a
field.  Here we apply that result to the case where $H$ and $Q$ are
elementary abelian $2$-groups and $\ch k=2$.  We then work out the
special case where $H$ has rank $4$, $Q$ has rank $2$, and $G$ is the
Burt Group of order $64$.  It was shown by Burt Totaro that the
spectral sequence arising from this extension could not collapse, but
using our methods we are able to obtain complete information on the
spectral sequence.