Bogomolov multipliers for unitriangular groups

TL;DR

This paper proves that the Bogomolov multiplier vanishes for various classes of unitriangular groups, resolving an open problem and contributing to the understanding of their cohomological properties.

Contribution

It provides a positive answer to an open problem by showing the Bogomolov multiplier is zero for several classes of unitriangular groups.

Findings

Bogomolov multiplier is zero for unitriangular groups over a field

Multiplier vanishes for quotients and subgroups of the lower central series

Result applies to central products of two unitriangular groups

Abstract

The Bogomolov multiplier $B_0(G)$ of a finite group $G$ is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of $G$. In this paper we give a positive answer to an open problem posed by Kang and Kunyavski\u{i} in \cite{KK}. Namely, we prove that if $G$ is either a unitriangular group over $\f$, a quotient of its lower central series, a subgroup of its lower central series, or a central product of two unitriangular groups, then $B_0(G)=0$.