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Isomorphic subgroups of solvable groups


Authors: I. M. Isaacs and Geoffrey R. Robinson
Journal: Proc. Amer. Math. Soc. 143 (2015), 3371-3376
MSC (2010): Primary 20D10
DOI: https://doi.org/10.1090/proc/12534
Published electronically: April 23, 2015
MathSciNet review: 3348779
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Abstract: Let $ H$ and $ K$ be isomorphic subgroups of a solvable group $ G$, and suppose that $ H$ is maximal in $ G$. We show that if either $ H$ is supersolvable, or a Sylow $ 2$-subgroup of $ H$ is abelian, then $ K$ is also maximal in $ G$.


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Additional Information

I. M. Isaacs
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: isaacs@math.wisc.edu

Geoffrey R. Robinson
Affiliation: Heilbronn Institute for Mathematical Research, University of Bristol, Bristol BS8 1TW, United Kingdom — and — Institute of Mathematics. University of Aberdeen, Aberdeen, AB24 3UE, Scotland
Email: g.r.robinson@abdn.ac.uk

DOI: https://doi.org/10.1090/proc/12534
Keywords: Solvable group, nilpotent injector, ZJ-Theorem, maximal subgroup
Received by editor(s): February 23, 2014
Received by editor(s) in revised form: March 24, 2014
Published electronically: April 23, 2015
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2015 American Mathematical Society