An exact sequence and triviality of Bogomolov multiplier of groups

2021/03/05 by Sumana Hatui, Hatui, Sumana
Mathematics · #13A50 #14E08 #14M20 #20D15 #20J06 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2103.03785

openalex publication_date 2021/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Bogomolov multiplier B₀(G) of a finite group G is the subgroup of the Schur multiplier H²(G,\mathbb Q/\mathbb Z) consisting of the cohomology classes which vanish after restricting to every abelian subgroup of G. We give a new proof of a Hopf-type formula for B₀(G) and derive an exact sequence for the cohomological version of the Bogomolov multiplier. Using this exact sequence we provide necessary and sufficient conditions for the corresponding inflation homomorphism to be an epimorphism and to be the zero map. Finally, we give a complete list of groups of order p⁶, for odd prime p, having trivial Bogomolov multiplier, so completing the 2020 investigation of Chen and Ma.

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