The Schur multiplier of finite symplectic groups

TL;DR

This paper determines that the Schur multiplier of finite symplectic groups over integers modulo D, where D is divisible by 4, is isomorphic to Z/2Z, providing a specific algebraic invariant for these groups.

Contribution

It establishes the exact structure of the Schur multiplier for symplectic groups over certain finite rings, a result not previously known.

Findings

Schur multiplier of Sp(2g, Z/DZ) is Z/2Z when D divisible by 4

Provides explicit computation of the Schur multiplier for these groups

Enhances understanding of the algebraic properties of finite symplectic groups

Abstract

We show that the Schur multiplier of $Sp(2g,\mathbb Z/D\mathbb Z)$ is $\mathbb Z/2\mathbb Z$, when $D$ is divisible by 4.