Unramified Brauer Groups of Finite and Infinite Groups
نویسنده
چکیده
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.
منابع مشابه
UNRAMIFIED BRAUER GROUPS OF FINITE SIMPLE GROUPS OF LIE TYPE Al FEDOR BOGOMOLOV, JORGE MACIEL, AND TIHOMIR PETROV
We study the subgroup B0(G) of H (G, Q/Z) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B0(G) is trivial for finite simple groups of Lie type Al.
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