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# Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Khukhro, Evgenii I. / Kramer, Linus

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1435-4446
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# On the intersection of certain maximal subgroups of a finite group

/ James C. Beidleman
/ Hermann Heineken
/ Matthew F. Ragland
/ Jack Schmidt
Published Online: 2013-11-23 | DOI: https://doi.org/10.1515/jgt-2013-0052

## Abstract.

Let $\Delta \left(G\right)$ denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which $G/\Delta \left(G\right)$ is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H.

## About the article

Published Online: 2013-11-23

Published in Print: 2014-07-01

Citation Information: Journal of Group Theory, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883,

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© 2014 by Walter de Gruyter Berlin/Boston.