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 non\(FC\). 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 non\(FC\). 10.1017/S0004972713000014

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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