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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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  • 1. A. Chermak and A. Delgado, A measuring argument for finite groups, Proc. Amer. Math. Soc. 107 (1989) 907-914. MR 90c:20001
  • 2. A. Lucchini, On the order of transitive permutation groups with cyclic point-stabilizer, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 9 (1998) 241-243. MR 2000k:20004
  • 3. V. I. Zenkov, Intersections of abelian subgroups in finite groups, Math. Notes 56 (1994) 869-871. MR 95m:20021

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Additional Information

I. M. Isaacs
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison, Wisconsin 53706

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