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Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q)

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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
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
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
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.