Moravec, Primož Unramified Brauer groups of finite and infinite groups. (English) Zbl 1346.20072 Am. J. Math. 134, No. 6, 1679-1704 (2012). Summary: The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramified Brauer group of a given quotient space. We derive a homological version of the Bogomolov multiplier, prove a Hopf-type formula, find a five term exact sequence corresponding to this invariant, and describe the role of the Bogomolov multiplier in the theory of central extensions. A new description of the Bogomolov multiplier of a nilpotent group of class two is obtained. We define the Bogomolov multiplier within \(K\)-theory and show that proving its triviality is equivalent to solving a long-standing problem posed by Bass. An algorithm for computing the Bogomolov multiplier is developed. Cited in 6 ReviewsCited in 30 Documents MSC: 20J05 Homological methods in group theory 14F22 Brauer groups of schemes 19C09 Central extensions and Schur multipliers Keywords:Bogomolov multipliers; unramified Brauer groups; central extensions Software:GAP PDFBibTeX XMLCite \textit{P. Moravec}, Am. J. Math. 134, No. 6, 1679--1704 (2012; Zbl 1346.20072) Full Text: DOI arXiv