Date of Award
2015
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Magliveras, Spyros S.
Abstract
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.
Extent
74 p.
Recommended Citation
Thapa, Magar Krishna B, "Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q)" (2015). Electronic Theses and Dissertations 2010 - 2019. 1257.
https://digitalcommons.fau.edu/etd_general_6/1257
Identifier
FA00004471
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2015|FAU Electronic Theses and Dissertations Collection|Includes bibliography.