Computing a spectral sequence of finite Heisenberg groups of prime power order

Abstract

Let p≥5 be a prime number, let n≥2 be a natural number and let Heis(pn) denote the Heisenberg group modulo pn. We study the Lyndon-Hochschild-Serre spectral sequence E(Heis(pn)) associated to Heis(pn) considered as a split extension, and show that, E(Heis(pn)) collapses in the third page. Moreover, for a fixed p, the spectral sequences E(Heis(pn)) are isomorphic as bigraded algebras from the second page on.