Pure Maths Colloquium: Simple groups, random generation, and algorithms for finitely presented groups
5 December 2016 16:00 in CM221
If one picks two elements at random in a finite non-abelian simple group G (such as an alternating group), then these two elements will generate G with probability tending to 1 as the order of G tends to infinity. I will discuss this result and variations, and show how they connect with some basic questions concerning the existence of algorithms that determine finite images of finitely presented groups. No specialist knowledge will be assumed.
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