SEMINAR: Groups and Combinatorics Seminar: Carlisle King, 4pm Oct 5 in Weatherburn LT
|Groups and Combinatorics Seminar: Carlisle King, 4pm Oct 5 in Weatherburn LT
Speaker: Carlisle King (University of Western Australia)
Title: Generation of finite simple groups
Time and place: 4pm Friday 5 Oct 2018, Weatherburn LT
Abstract: Let G be a finite simple group. It is well-known that G is generated by a pair of elements – we say G is 2-generated. It has been shown that 2 elements chosen at random from G generate G with probability tending to 1 as |G| tends to infinity. A natural refinement is to ask, given a pair of integers (a,b), whether G is 2-generated by an element of order a and an element of order b. If such a pair exists, we say that G is (a,b)-generated. We will explore some past results regarding (2,3)-generation proved using probabilistic methods, as well as a recent result on (2,p)-generation for some prime p.
An equivalent statement of the 2-generation theorem is that every finite simple is an image of F2, the free group on 2 generators. More generally, given a finitely presented group Gamma, one can ask which finite simple groups are images of Gamma. We will study a new result in this area concerning the free product Gamma=A*B of nontrivial finite groups A and B, also proved using probabilistic methods.
For past and future seminars see
Fri, 05 Oct 2018 16:00
Fri, 05 Oct 2018 17:00
Stephen Glasby <[email protected]>
Tue, 02 Oct 2018 09:08
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