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University of Sydney Algebra Seminar

Kamilla Rekvenyi

Friday 14 February, 12-1pm, in Carslaw 275

Width questions in finite simple groups

Let \(T\) be a non-abelian simple group, and \(S\) a generating set of \(T\). Define the width of \(T\) with respect to \(S\), to be \( \min \{k : S^k=T\},\) where \(S^k \) is the set of products of \(k\) elements in \(S\). Finding this number has been considered with respect to several generating sets, for example the case where \(S\) is a conjugacy class or the case when \(S\) is the set of involutions in \(T\). I will mention some of these and a new result, in collaboration with D. Dona and M. Liebeck, which is a refinement of width questions in finite simple groups.