On the theory of generalized FC-groups

JOURNAL OF ALGEBRA

卷:326

Article

Robinson, Derek J. S.¹  Russo, Alessio²  Vincenzi, Giovanni³ 

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Univ Naples 2, Dipartimento Matemat, I-81100 Caserta, Italy

[3] Univ Salerno, Dipartimento Matemat & Informat, I-84084 Fisciano Salerno, Italy

关键词: Generalized FC-group;    Profinite topology;   

DOI  :  10.1016/j.jalgebra.2009.04.002

来源: Elsevier

【 摘 要 】

We extend to FC*, the class of generalized FC-groups introduced in [F. de Giovanni, A. Russo, G. Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J. 28 (2002) 241-254], some results known for FC-groups. The main theorem involves the extended residually finite property (ERF), i.e., all subgroups are closed in the profinite topology. The ERF-groups belonging to several large classes of groups have been determined, for example nilpotent groups [M. Menth, Nilpotent groups with every quotient residually finite, J. Group Theory 5 (2002) 199-217] and FC-groups [D.J.S. Robinson, A. Russo, G. Vincenzi, On groups whose subgroups are closed in the profinite topology. J. Pure Appl. Algebra 213 (2009) 421-429]. Here we generalize these results by classifying completely the ERF-groups belonging to FC*. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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