The width of a group
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 Nick Gill (Open University)
 Wednesday 28 November 2012, 14:3015:00
 MR11, CMS.
If you have a question about this talk, please contact Ben Green.
I describe recent work with Pyber, Short and Szabo in which we study the
`width’ of a finite simple group. Given a group G and a subset A of G, the
`width of G with respect to A’ – w(G,A) – is the smallest number k such that G
can be written as the product of k conjugates of A. If G is finite and simple,
and A is a set of size at least 2, then w(G,A) is welldefined; what is more
Liebeck, Nikolov and Shalev have conjectured that in this situation there
exists an absolute constant c such that w(G,A)\leq c logG/logA.
I will present a partial proof of this conjecture as well as describing some
interesting, and unexpected, connections between this work and classical
additive combinatorics. In particular the notion of a normal Kapproximate
group will be introduced.
This talk is part of the Discrete Analysis Seminar series.
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