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Sharply $2$-transitive groups with point stabilizer of exponent $3$ or $6$

Author: Peter Mayr
Journal: Proc. Amer. Math. Soc. 134 (2006), 9-13
MSC (2000): Primary 20B20; Secondary 20B22
Published electronically: August 15, 2005
MathSciNet review: 2170537
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Abstract: Using the fact that all groups of exponent $3$ are nilpotent, we show that every sharply $2$-transitive permutation group whose point stabilizer has exponent $3$ or $6$ is finite.

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Additional Information

Peter Mayr
Affiliation: Institut für Algebra, Johannes Kepler Universität Linz, 4040 Linz, Austria

Keywords: (Infinite) sharply $2$-transitive groups
Received by editor(s): July 21, 2004
Published electronically: August 15, 2005
Additional Notes: This work was supported by grant P15691 of the Austrian National Science Foundation (FWF) and was obtained during the author’s visit at UW Madison, Wisconsin.
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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