Schur multipliers of unitriangular groups

TL;DR

This paper derives an explicit formula for the Schur multiplier of unitriangular matrix groups over cyclic rings and integers, enabling new insights into their structure and covering groups.

Contribution

It provides a new explicit formula for the Schur multiplier of unitriangular groups over specific rings, advancing understanding of their algebraic properties.

Findings

Explicit formula for Schur multipliers over cyclic rings and integers

Presentations of covering groups of these unitriangular groups

Discussion on nonisomorphic representatives of covering groups

Abstract

An explicit formula for the Schur multiplier of the group of unitriangular matrices over products of cyclic rings $\ZZ/m\ZZ$ and $\ZZ$ is derived. We use it to provide presentations of the corresponding covering groups and touch upon the question of finding their nonisomorphic representatives.