A note on groups with restrictions on centralizers of infinite index

Summary: A group $G$ is said to be an $AFC$-group if for each element $x$ of $G$, either $x$ has finitely many conjugates or the factor group $C_G(x)/\langle x\rangle$ is finite. In this survey article some results concerning $AFC$-groups and minimal-non-$AFC$ groups are collected.

Country

Italy

Related Organizations

University Federico II of Naples
Italy
University of Salento
Italy

Keywords

minimal-non-$AFC$ group, General structure theorems for groups, $FC$-centre, minimal-non-$AFC$ group, $AFC$-group, FC-groups and their generalizations, $AFC$-group, 610, $FC$-centre, 510, Conjugacy classes for groups

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