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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Abelian point stabilizers in transitive permutation groups


Author: I. M. Isaacs
Journal: Proc. Amer. Math. Soc. 130 (2002), 1923-1925
MSC (2000): Primary 20B05, 20D99
Published electronically: November 15, 2001
MathSciNet review: 1896023
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06400-0
PII: S 0002-9939(01)06400-0
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
Article copyright: © Copyright 2001 American Mathematical Society