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 (Formula presented.) is finite and (Formula presented.) 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.
Groups in which every element has a paracentralizer of finite index / De Falco, M.; Evans, M. J.; de Giovanni, F.; Musella, C.. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 48:5(2020), pp. 2160-2166. [10.1080/00927872.2019.1710179]
Groups in which every element has a paracentralizer of finite index
De Falco M.;Evans M. J.;de Giovanni F.;Musella C.
2020
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 (Formula presented.) is finite and (Formula presented.) 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
