Projective representations of Heisenberg groups over the rings of order p^2

Abstract

In this article we describe the 2-cocycles, Schur multiplier and representation group of discrete Heisenberg groups over the unital rings of order $p^2$. We describe all projective representations of Heisenberg groups with entries from the rings $\mathbb Z/p^2\mathbb Z$ and $\mathbb{F}_p[t]/(t^2)$ and obtain a classification of their degenerate and non-degenerate 2-cocycles.