A differential in the Lyndon—Hochschild—Serre spectral sequence

AbstractWe consider the Lyndon-Hochschild-Serre spectral sequence with Fn coefficients for a central extension with kernel cyclic of order a power of p and arbitrary discrete quotient group. For this spectral sequence d2 and d3 are known, and we give a description for d4. Using this result we deduce a similar formula for the Serre spectral sequence for a fibration with fibre BCpn. The differential from odd rows to even rows involves a Massey triple product, so we describe the calculation of such products in the cohomology of a finite abelian group. As an example we determine the Poincaré series for the mod-3 cohomology of various 3-groups