Exponents of Bogomolov multipliers

TL;DR

This paper establishes conditions under which the exponent of a finite group's Bogomolov multiplier divides the group's exponent, covering cases like metabelian, exponent 4, nilpotent of class ≤5, and 4-Engel groups.

Contribution

It proves that the exponent of the Bogomolov multiplier divides the group's exponent in four specific classes of finite groups, extending understanding of these algebraic structures.

Findings

Exponent divides in metabelian groups

Exponent divides when exponent is 4

Exponent divides for nilpotent groups of class ≤5

Abstract

We prove that if $G$ is a finite group, then the exponent of its Bogomolov multiplier divides the exponent of $G$ in the following four cases: (i) $G$ is metabelian, (ii) $\exp G=4$, (iii) $G$ is nilpotent of class $\le 5$, or (iv) $G$ is a $4$-Engel group.