Local control and Bogomolov multipliers of finite groups

TL;DR

This paper investigates the properties of the Bogomolov multiplier in finite groups, demonstrating that under certain nilpotency conditions on Sylow p-subgroups, the p-part of this multiplier exhibits local control.

Contribution

It establishes a new connection between the nilpotency class of Sylow p-subgroups and the local control of the p-part of the Bogomolov multiplier in finite groups.

Findings

p-part of Bogomolov multiplier is locally controlled under specified conditions

Nilpotency class at most p implies local control of the p-part

Provides new insights into the structure of Bogomolov multipliers

Abstract

We show that if a Sylow $p$-subgroup of a finite group $G$ is nilpotent of class at most $p$, then the $p$-part of the Bogomolov multiplier of $G$ is locally controlled.