Groups with small cocentralizers

Javier Otal, Nikolaj N. Semko


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.


Cocentralizer in a group. Groups with prescribed conjugacy classes: \(FC\)-groups. \(CC\)-groups. \(PC\)-groups. \(MC\)-groups

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