Let G be a finite permutation group acting on a finite set Ω. Then we denote by σk(G,Ω) the number of G-orbits on the set Ωk, consisting of all k-subsets of Ω. In this thesis we develop methods for calculating the values for σk(G,Ω) and produce formulae for the cases that G is a doubly-transitive simple rank one Lie type group. That is G ∼ = PSL(2,q),Sz(q),PSU(3,q) or R(q). We also give reduced functions for the calculation of the number of orbits of these groups when k = 3 and go on to consider the numbers of orbits, when G is a finite abelian group in its regular representation. We then consider orbit lengths and examine groups with “large” G-orbits on subsetsof size 3.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:632257 |
| Date | January 2014 |
| Creators | Bradley, Paul Michael |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/counting-gorbits-on-the-induced-action-on-ksubsets(bd41f2da-eb59-4a6b-bf58-84954ccb9621).html |
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