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GROUPS OF INFINITE RANK IN WHICH NORMALITY IS A TRANSITIVE RELATION

Published online by Cambridge University Press:  30 August 2013

M. DE FALCO ,
F. DE GIOVANNI ,
C. MUSELLA  and
Y. P. SYSAK
M. DE FALCO
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II Complesso Universitario Monte S. Angelo, Via Cintia, I – 80126 Napoli, Italy e-mail: degiovan@unina.it, mdefalco@unina.it, cmusella@unina.it
F. DE GIOVANNI
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II Complesso Universitario Monte S. Angelo, Via Cintia, I – 80126 Napoli, Italy e-mail: degiovan@unina.it, mdefalco@unina.it, cmusella@unina.it
C. MUSELLA
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II Complesso Universitario Monte S. Angelo, Via Cintia, I – 80126 Napoli, Italy e-mail: degiovan@unina.it, mdefalco@unina.it, cmusella@unina.it
Y. P. SYSAK
Affiliation:
Institute of Mathematics, Ukrainian National Academy of Sciences vul. Tereshchenkivska 3, 01601 Kiev, Ukraine e-mail: sysak@imath.kiev.ua
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Abstract

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A group is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is a periodic (generalized) soluble group in which all subnormal subgroups of infinite rank are normal, then either G is a T-group or it has finite rank. It follows that if G is an arbitrary group whose Fitting subgroup has infinite rank, then G has the property T if and only if all its subnormal subgroups of infinite rank are normal.

Keywords

20E15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 387 - 393
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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