AG Algebra, Geometrie und Computeralgebra

Melissa Lee, Imperial College London: Bases of almost quasisimple groups and Pyber's conjecture


Vortrag im Oberseminar der AG Algebra, Geometrie und Computeralgebra

Referentin: Melissa Lee, Imperial College London

Zeit: Donnerstag 25.10.2018, 17:00 Uhr

Ort: Raum 48-436

Abstract: A base of a permutation group G acting on Ω is a subset of Ω whose pointwise stabiliser in G is trivial. Bases have their origins in computational group theory, where they were used to efficiently store permutation groups of large degree into a small amount of computer memory. The minimal base size of G is denoted by b(G). When b(G) = 1, we say that G has a regular orbit on Ω.

A well-known conjecture made by Pyber in 1993 states that there is an absolute constant c such that if G acts primitively on Ω, then b(G) < c log |G| / log n, where |Ω| = n. Pyber's conjecture was established in 2016 by Duyan, Halasi and Maroti, following on from contributions from a variety of authors.

In this talk, I will cover some of the history and uses of bases, and discuss Pyber's conjecture, as well as present some results on the determination of the constant c for bases of almost quasisimple linear groups. I will also outline some recent work on determining which irreducible modules of linear groups contain a regular orbit.

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