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The structure of finite groups in which permutability is a transitive relation

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Derek J. S. Robinson
Derek J. S. Robinson
Affiliation:
Department of Mathematics University of Illinois in Urbana-Champaign1409 West Green Street Urbana IL 61801USA e-mail: robinson@math.uiuc.edu
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Abstract

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The structure of finite groups in which permutability is transitive (PT-groups) is studied in detail. In particular a finite PT-group has simple chief factors and the p-chief factors fall into at most two isomorphism classes. The structure of finite T-groups, that is, groups in which normality is transitive, is also discussed, as is that of groups generated by subnormal or normal PT-subgroups.

MSC classification

Secondary: 20D35: Subnormal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 2 , April 2001 , pp. 143 - 160
Copyright
Copyright © Australian Mathematical Society 2001

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