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Type of Document	Dissertation
Author	Keller, Gordon Ernest
URN	etd-04142003-092438
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-04142003-092438
Title	Groups with only the identity fixing three letters
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Unknown Committee Member
Keywords	None
Date of Defense	1965-04-05
Availability	unrestricted
Abstract In this paper, we study finite transitive permutation groups in which only the identity fixes as many as three letters, and in which the subgroup fixing a letter is self normalizing. If G is such a group, the principal results concern the case when G is simple. In this case, H, the subgroup fixing a letter, is a Frobenius group, MQ, with kernel M and complement Q. If |H| is even we show that either G is doubly transitive or permutation isomorphic to the representation of A[subscript 5] on ten letters. If |H| is odd we prove that Q is cyclic, M is a p-group, and G has a single class of involutions. Furthermore, the number of groups for which H has a given positive number of regular orbits is finite.
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