Bogomolov multipliers for 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 Kunyavskiĭ 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 $B_0(G)=0$.

Some errors are corrected in v2

References in corpus (4)

• Noether's problem and unramified Brauer groups
• Unramified Brauer groups for groups of order p^5
• The Bogomolov multiplier of rigid finite groups
• Groups of order $p^5$ and their unramified Brauer groups

Cited by in corpus (2)

• The Massey vanishing conjecture for number fields
• The Bogomolov multiplier of Lie algebras