Isomorphic subgroups of solvable groups
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- by I. M. Isaacs and Geoffrey R. Robinson PDF
- Proc. Amer. Math. Soc. 143 (2015), 3371-3376 Request permission
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 $G$.References
- George Glauberman, A characteristic subgroup of a $p$-stable group, Canadian J. Math. 20 (1968), 1101–1135. MR 230807, DOI 10.4153/CJM-1968-107-2
- Hans Lausch, Conjugacy classes of maximal nilpotent subgroups, Israel J. Math. 47 (1984), no. 1, 29–31. MR 736062, DOI 10.1007/BF02760560
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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3371-3376
- MSC (2010): Primary 20D10
- DOI: https://doi.org/10.1090/proc/12534
- MathSciNet review: 3348779