Groups whose proper subgroups have restricted infinite conjugacy classes
Volume 150 / 2017
Colloquium Mathematicum 150 (2017), 281-291
MSC: Primary 20F24.
DOI: 10.4064/cm7015-1-2017
Published online: 29 September 2017
Abstract
A group $G$ is said to have the $\mathit{AFC} $-property if for each element $x$ of $G$ at least one of the indices $|G:C_G(x)|$ and $|C_G(x):\langle x\rangle|$ is finite. The class of $\mathit{AFC} $-groups, which generalize $\mathit{FC} $-groups, has been studied by De Falco et al. (2017) and Shalev (1994). Here the structure of groups whose proper subgroups have the $\mathit{AFC} $-property is investigated.
