Permutation groups and induced actions on k-subsets

  • Awatef Almotairi

Student thesis: Phd


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.
Date of Award1 Aug 2020
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorPeter Rowley (Supervisor) & Yuri Bazlov (Supervisor)


  • Group Theory
  • permutation group
  • orbits
  • k-subsets

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