Groups of order $p^5$ and their unramified Brauer groups
We classify all groups of order $p^5$ with non-trivial unramified Brauer groups. We show that if $p>3$, then there are precisely $\gcd (p-1,4)+\gcd (p-1,3)+1$ such groups.
math.GR↗
arXiv subjects
Primoz Moravec
Publications and source records attributed to Primoz Moravec.
Unramified Brauer groups of finite and infinite groups
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.
math.GR↗
Unramified Brauer groups and isoclinism
We show that if $G_1$ and $G_2$ are isoclinic groups, then their Bogomolov multipliers are isomorphic.
math.GR↗