This article is cited in 3 papers

SURVEY ARTICLE

Groups with small cocentralizers

Javier Otal^a, Nikolaj N.Semko<sup>b

a</sup> Departamento de Matemáticas — IUMA, Universidad de Zaragoza, Pedro Cerbuna 12. 50009 Zaragoza, SPAIN
^b Department of Mathematics, National State Tax Service Academy of Ukraine, 09200 Irpen, UKRAINE.

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.

Keywords: Cocentralizer in a group. Groups with prescribed conjugacy classes: $FC$–groups. $CC$–groups. $PC$–groups. $MC$–groups.

MSC: 20F24, 20F17

Received: 07.07.2009
Revised: 07.07.2009

Language: English

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