Groups with small cocentralizers

Abstract

Let \(G\) be a group. If \(S\subseteq G\) is a \(G\)-invariant subset of \(G\), the factor-group \(G/C_G(S)\) is called the cocentralizer of \(S\) in \(G\). In this survey-paper we review some results dealing with the influence of several cocentralizers on the structure of the group, a direction of research to which Leonid A. Kurdachenko was an active contributor, as well as many mathematicians all around the world.