Citation
Keller, Gordon Ernest (1965) Groups with Only the Identity Fixing Three Letters. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GVHG-EC49. https://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.)) |
---|---|
Subject Keywords: | (Mathematics) |
Degree Grantor: | California Institute of Technology |
Division: | Physics, Mathematics and Astronomy |
Major Option: | Mathematics |
Thesis Availability: | Public (worldwide access) |
Research Advisor(s): |
|
Thesis Committee: |
|
Defense Date: | 5 April 1965 |
Record Number: | CaltechETD:etd-04142003-092438 |
Persistent URL: | https://resolver.caltech.edu/CaltechETD:etd-04142003-092438 |
DOI: | 10.7907/GVHG-EC49 |
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: | 08 Feb 2024 22:59 |
Thesis Files
|
PDF (Keller_ge_1965.pdf)
- Final Version
See Usage Policy. 2MB |
Repository Staff Only: item control page