Abelian point stabilizers in transitive permutation groups
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Abstract:
In this note we prove that if the point stabilizer $A$ in a transitive permutation group of degree $m$ is abelian, then the exponent of $A$ is less than $m$. This extends an earlier result of Andrea Lucchini, who proved this in the case where $A$ is cyclic.References
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Additional Information
- I. M. Isaacs
- Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison, Wisconsin 53706
- Email: isaacs@math.wisc.edu
- Received by editor(s): January 30, 2001
- Published electronically: November 15, 2001
- Additional Notes: Research partially supported by a grant from the U. S. National Security Agency
- Communicated by: Stephen D. Smith
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1923-1925
- MSC (2000): Primary 20B05, 20D99
- DOI: https://doi.org/10.1090/S0002-9939-01-06400-0
- MathSciNet review: 1896023