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SEMINAR: Groups and Combinatorics Seminar 16:00 Fri 23/02/2018 Robert Street LT: Scott Harper (Univ. of Bristol)

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Today's date is Friday, November 27, 2020
Groups and Combinatorics Seminar 16:00 Fri 23/02/2018 Robert Street LT: Scott Harper (Univ. of Bristol) Other events...
Speaker: Scott Harper (University of Bristol)

Title: Uniform Domination for Simple Groups

Time and place: 16:00 Friday 23/02/2018 in Robert Street LT

Abstract: It is well known that every finite simple group can be generated by just two elements. In fact, by a theorem of Guralnick and Kantor, there is a conjugacy class C such that for each non-identity element x there exists an element y in C such that x and y generate the entire group. Motivated by this, we introduce a new invariant for finite groups: the uniform domination number. This is the minimal size of a subset S of conjugate elements such that for each non-identity element x there exists an element s in S such that x and s generate the group. This invariant arises naturally in the study of generating graphs.

In this talk, I will present recent joint work with Tim Burness, which establishes best possible results on the uniform domination number for finite simple groups, using a mix of probabilistic and computational methods, together with recent results on the base sizes of primitive permutation groups.

Past and future seminars may be found at https://www.maths.uwa.edu.au/~glasby/GroupsAndCombinatoricsSeminar/S18.html

There will be cake in the Mathematics and Statistics tea room at 15:40. The seminar starts at 16:00, and after 17:05 we go to the UniClub or Student Tavern for a drink.
Contact Stephen Glasby <[email protected]>
Start Fri, 23 Feb 2018 16:00
End Fri, 23 Feb 2018 17:00
Submitted by Stephen Glasby <[email protected]>
Last Updated Mon, 19 Feb 2018 10:41
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