# Unramified Brauer groups of finite and infinite groups

```@article{Moravec2012UnramifiedBG,
title={Unramified Brauer groups of finite and infinite groups},
author={Primoz Moravec},
journal={American Journal of Mathematics},
year={2012},
volume={134},
pages={1679 - 1704}
}```
• P. Moravec
• Published 14 March 2012
• Mathematics
• American Journal of Mathematics
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…

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