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Title: Permutation groups and induced actions on k-subsets
Author: Almotairi, Awatef
ISNI:       0000 0004 8505 1279
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2020
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Assume that G is a permutation group acting upon a set S of size n. Then a group action of G induces an action on S_k, the set of all k-subsets of S. In this thesis we derive a formulae to calculate the number of G-orbits on S_k where G is the group PSL(3,q) on its action upon q^2+q+1 points of the projective plane over GF(q). Also we investigate the situation when a G-orbit of a k-subset is of the maximal length |G| and all (k+1)-subsets encompassing it are of lengths less than |G|. We examine this case when G is the group PSL(2,q) in its action on the projective line of q+1 points. We subsequently pay attention to count the G-orbits on S_k for several primitive groups of small degrees.
Supervisor: Rowley, Peter ; Bazlov, Yuri Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: k-subsets ; orbits ; Group Theory ; permutation group