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PRONORMALITY IN GENERALIZED FC-GROUPS

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  14 September 2010

E. ROMANO  and
G. VINCENZI
E. ROMANO
Affiliation:
Dipartimento di Matematica e Informatica, Università di Salerno, Salerno, Italy (email: eromano@unisa.it)
G. VINCENZI*
Affiliation:
Dipartimento di Matematica e Informatica, Università di Salerno, Salerno, Italy (email: gvincenzi@unisa.it)
*
✉For correspondence; e-mail: gvincenzi@unisa.it
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Abstract

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We extend some results known for FC-groups to the class FC* of generalized FC-groups introduced in de Giovanni et al. [‘Groups with restricted conjugacy classes’, Serdica Math. J.28(3) (2002), 241–254]. The main theorems pertain to the join of pronormal subgroups. The relevant role that the Wielandt subgroup plays in an FC*-group is pointed out.

Keywords

generalized FC-groupspronormalityWielandt subgroup

MSC classification

Secondary: 20E34: General structure theorems 20F19: Generalizations of solvable and nilpotent groups 20F24: FC-groups and their generalizations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 2 , April 2011 , pp. 220 - 230
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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