CEU Electronic Theses and Dissertations, 2020
| Author | Duyan, Hülya |
|---|---|
| Title | Bounds of Some Invariants of Finite Permutation Groups |
| Summary | The first three chapters discuss base size and Pyber's conjecture. The first chapter introduces the concept of distinguishing number for transitive permutation groups. The second chapter provides state-of-the-art information on the base size, in particular on that of primitive permutation groups. In the third chapter we prove Pyber's conjecture for affine type primitive groups, the only remaining class of primitive groups for which the conjecture has not been verified. The proof relies on a bound on the distinguishing number of transitive permutation groups. In the last chapter we discuss random bases for coprime primitive linear groups. We show that if G is a coprime primitive linear group in GL(V) then the probability that a random 11-tuple in V is a base for G tends to 1 as the size of V approaches infinity. |
| Supervisor | Halasi, Zoltán |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2020/duyan_hulya.pdf |
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