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

Abstract

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