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Unramified Brauer groups of finite and infinite groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 134, Number 6, December 2012
- pp. 1679-1704
- 10.1353/ajm.2012.0046
- Article
- Additional Information
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.