Locally finite groups whose subgroups have finite normal oscillation

Authors

  • F. de Giovanni University of Napoli "Federico II"
  • M. Martusciello University of Napoli "Federico II"
  • C. Rainone University of Napoli "Federico II"

Keywords:

locally finite group, normal oscillation

Abstract

If \(X\) is a subgroup of a group \(G\), the cardinal number \(min\{ |X:X_G|,X^G:X|\}\) is called the normal oscillation of \(X\) in \(G\). It is proved that if all subgroups of a locally finite group \(G\) have finite normal oscillation, then \(G\) contains a nilpotent subgroup of finite index. DOI: 10.1017/S000497271300097X

Author Biographies

F. de Giovanni, University of Napoli "Federico II"

Dipartimento di Matematica e Applicazioni - full professor

M. Martusciello, University of Napoli "Federico II"

Dipartimento di Matematica e Applicazioni - PhD

C. Rainone, University of Napoli "Federico II"

Dipartimento di Matematica e Applicazioni - PhD

Published

2014-03-25

Issue

Vol. 89 No. 3 (2014)

Section

Articles
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