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.
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/813361
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