The cohomology of split extensions of elementary abelian 2-groups and Totaroʹs example Original Research Article

In a previous paper we derived an expression for the differentials in the Lyndon–Hochschild–Serre spectral sequence of a split extension G=H times sign, right closed 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 char k=2. We then work out a special case, in which H has rank 4 and Q has rank 2, from a class of examples constructed by Burt Totaro. Totaro proved 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.