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Groups with only the identity fixing three letters

Citation

Keller, Gordon Ernest (1965) Groups with only the identity fixing three letters. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-04142003-092438

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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hall, Marshall
Thesis Committee:
  • Unknown, Unknown
Defense Date:5 April 1965
Record Number:CaltechETD:etd-04142003-092438
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-04142003-092438
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1377
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:15 Apr 2003
Last Modified:26 Dec 2012 02:37

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