Journal of Algebra | 2019
On Bogomolov multiplier and Ш-rigidity of groups
Abstract
Abstract We show the existence of groups with trivial Bogomolov multiplier such that the Bogomolov multiplier of a central product of these groups is non-trivial. We then prove that finite quasisimple groups and freest special p-groups are Ш-rigid in the sense that all their class-preserving automorphisms are inner. As an application we show the existence of non-nilpotent Ш-rigid groups and Ш-rigid p-groups of odd order having non-trivial Bogomolov multiplier.