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Permutation groups and induced actions on k-subsets

Almotairi, Awatef Hoidi A

[Thesis]. Manchester, UK: The University of Manchester; 2020.

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Abstract

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.

Bibliographic metadata

Type of resource:
Content type:
Form of thesis:
Type of submission:
Degree type:
Doctor of Philosophy
Degree programme:
PhD Mathematical Sciences
Publication date:
Location:
Manchester, UK
Total pages:
124
Abstract:
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.
Thesis main supervisor(s):
Thesis co-supervisor(s):
Language:
en

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:323662
Created by:
Almotairi, Awatef
Created:
13th February, 2020, 12:52:35
Last modified by:
Almotairi, Awatef
Last modified:
2nd March, 2020, 10:55:37

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