Cameron-Liebler Sets for 2-Transitive Groups

This research was conducted on 2-transitive groups whose minimal normal subgroup is abelian. Suppose G is such a group and ΓG is its derangement graph. Any maximum coclique S of ΓG has a characteristic vector xS. Each xS is a boolean vector contained in a particular module, which is called the permutation module MP. This module has a dimension of 1 + (n − 1)2, where n = deg(G), and it is spanned by {xij | i,j∈{1,...,n}}, where each xij is the characteristic vector of Sij, the set of permutations that map i to j. Apart from the xij, which correspond to the stabilizers of G and their cosets, this research set out to find any other boolean vectors that are contained in Mp using linear programming. Henceforth, such boolean vectors are defined to be Cameron-Liebler sets for 2-transitive groups. In addition to finding Cameron-Liebler sets, analyses were performed on each group to determine: (1) whether the strict EKR property holds; (2) the number of maximum cocliques that are subgroups, cosets, or neither; (3) isomorphism classes and conjugacy classes of the maximum cocliques that are subgroups; (4) the dimension of C′, the maximum cliques that are subgroups (along with their right cosets), and C, all maximum cliques; and (5) the spectrum of ΓG and whether the ratio bound is satisfied with equality.

Name thesis:degree_name

Master of Science (MSc)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2020

Author dc:creator

• Palmarin, Daniel Michael

Advisors dc:contributor.advisor

• Fallat, Shaun
• Meagher, Karen

Committee member dc:contributor.committeemember

• Herman, Allen

Language dc:language.iso

en

DOI

https://doi.org/10.82465/4707

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/14360