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Groups with only the identity fixing three letters


Keller, Gordon Ernest (1965) Groups with only the identity fixing three letters. Dissertation (Ph.D.), California Institute of Technology.


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:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1377
Deposited By: Imported from ETD-db
Deposited On:15 Apr 2003
Last Modified:26 Dec 2012 02:37

Thesis Files

PDF (Keller_ge_1965.pdf) - Final Version
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