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


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