The Bogomolov multiplier of finite simple groups

TL;DR

This paper investigates the Bogomolov multiplier of finite simple groups, proving it is trivial for most cases except certain covers of PSL(3,4), thus advancing understanding of group cohomology.

Contribution

It establishes the triviality of the Bogomolov multiplier for quasisimple and almost simple groups, except for specific covers of PSL(3,4).

Findings

Bogomolov multiplier is trivial for most finite simple groups.

Exceptions occur in certain covers of PSL(3,4).

Provides new insights into the structure of group cohomology.

Abstract

The subgroup of the Schur multiplier of a finite group G consisting of all cohomology classes whose restriction to any abelian subgroup of G is zero is called the Bogomolov multiplier of G. We prove that if G is quasisimple or almost simple, its Bogomolov multiplier is trivial except for the case of certain covers of PSL(3,4).