Groups in which every element has a paracentralizer of finite index. Issue 5 (3rd May 2020)

• Record Type: Journal Article
• Authors: De Falco, M.; Evans, M. J.; de Giovanni, F.; Musella, C.
• Is Part Of: Communications in algebra. Volume 48:Issue 5(2020)
• Page Start: 2160
• Page End: 2166
• Publication Date: 2020-05-03
• Subjects: FC-group -- FP-group -- paracentralizer -- power automorphism; 20F24; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1710179
• Languages: English
• ISSNs: 0092-7872

Abstract

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