Bogomolov multipliers for unitriangular groups
Ivo Michailov Michailov

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 of a finite group is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of . 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 is either a unitriangular group over , a quotient of its lower central series, a subgroup of its lower central series, or a central product of two unitriangular groups, then .
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Taxonomy
TopicsFinite Group Theory Research · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
