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Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q)
- Date Issued:
- 2015
- Summary:
- Every transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then investigate the construction of rank-3 transitive and primitive extensions of a simple group, such that the extension group formed is also simple. In the latter context we present a new, group theoretic construction of the famous Hoffman-Singleton graph as a rank-3 graph.
Title: | Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q). |
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Name(s): |
Thapa Magar, Krishna B., author Magliveras, Spyros S., Thesis advisor Florida Atlantic University, Degree grantor Charles E. Schmidt College of Science Department of Mathematical Sciences |
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Type of Resource: | text | |
Genre: | Electronic Thesis Or Dissertation | |
Date Created: | 2015 | |
Date Issued: | 2015 | |
Publisher: | Florida Atlantic University | |
Place of Publication: | Boca Raton, Fla. | |
Physical Form: | application/pdf | |
Extent: | 74 p. | |
Language(s): | English | |
Summary: | Every transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then investigate the construction of rank-3 transitive and primitive extensions of a simple group, such that the extension group formed is also simple. In the latter context we present a new, group theoretic construction of the famous Hoffman-Singleton graph as a rank-3 graph. | |
Identifier: | FA00004471 (IID) | |
Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2015 | |
Collection: | FAU Electronic Theses and Dissertations Collection | |
Note(s): | Includes bibliography. | |
Subject(s): |
Combinatorial designs and configurations Cryptography Data encryption (Computer science) Finite geometries Finite groups Group theory Permutation groups |
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Held by: | Florida Atlantic University Libraries | |
Sublocation: | Digital Library | |
Links: | http://purl.flvc.org/fau/fd/FA00004471 | |
Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00004471 | |
Use and Reproduction: | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
Host Institution: | FAU | |
Is Part of Series: | Florida Atlantic University Digital Library Collections. |