Groups in which every element has a paracentralizer of finite index. Issue 5 (3rd May 2020) - De Falco, M.; Evans, M. J.; de Giovanni, F.; Musella, C.
Abstract: A group G is called an FP -group if for each element g of G there exists a subgroup Xg of G such that the index | G : X g | is finite and Y g = Y for all subgroups Y of Xg, that is, if every element of G induces by conjugation a power automorphism on a suitable subgroup of finite index of G . Thus groups with finite conjugacy classes have the FP -property, and the aim of this article is to study the behavior of FP -groups in relation to the known theory of FC -groups. Communicated by Sudarshan Kumar Sehgal