Projective representations of Heisenberg groups over the rings of order 𝑝2

Abstract

Abstract We describe the 2-cocycles, Schur multiplier and representation group of discrete Heisenberg groups over the unital rings of order p 2 p^{2} . We also describe all projective representations of Heisenberg groups with entries from the rings Z / p 2 ⁢ Z \mathbb{Z}/p^{2}\mathbb{Z} and F p ⁢ [ t ] / ( t 2 ) \mathbb{F}_{p}[t]/(t^{2}) for odd primes 𝑝 and obtain a classification of their degenerate and non-degenerate 2-cocycles.