On the Intersection of Certain Maximal Subgroups of a Finite Group

Authors

Adolfo Ballester-Bolinches, University de València, Spain
James C. Beidleman, University of KentuckyFollow
Hermann Heineken, Universität Würzburg, Germany
Matthew F. Ragland, Auburn University at Montgomery
Jack Schmidt, University of KentuckyFollow

Abstract

Let Δ(G) 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/Δ(G) 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.

Document Type

Article

Publication Date

7-2014

Notes/Citation Information

Published in Journal of Group Theory, v. 17, no. 4, p. 705-715.

© de Gruyter 2014

The copyright holders have granted the permission for posting the article here.

Digital Object Identifier (DOI)

http://dx.doi.org/10.1515/jgt-2013-0052

Repository Citation

Ballester-Bolinches, Adolfo; Beidleman, James C.; Heineken, Hermann; Ragland, Matthew F.; and Schmidt, Jack, "On the Intersection of Certain Maximal Subgroups of a Finite Group" (2014). Mathematics Faculty Publications. 11.
https://uknowledge.uky.edu/math_facpub/11