Groups whose proper subgroups of infinite rank have finite conjugacy classes

Authors

  • M. De Falco Università di Napoli "Federico II"
  • F. De Giovanni Università di Napoli "Federico II"
  • C. Musella Università di Napoli "Federico II"
  • N. Trabelsi University of Setif

Keywords:

Finite rank, FC-groups

Abstract

A group G is said to be an FC-group if each element of G has only finitely many conjugates, and G is minimal nonFC if all its proper subgroups have the property FC but G is not an FC-group. It is an open question whether there exists a group of infinite rank which is minimal nonFC. We consider here groups of infinite rank in which all proper subgroups of infinite rank are FC, and prove that in most cases such groups are either FC-groups or minimal nonFC. 10.1017/S0004972713000014

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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