What does a random finitely generated abelian group look like?

Alex Bartel (University of Glasgow)

Wednesday 11th October, 2017 16:00-17:00 Maths 311B


A general principle in pure mathematics, with many concrete known or conjectured instances, is that a random algebraic object is isomorphic to a given object X with probability that is inversely proportional to #Aut X. However, in the context of the title, this does not appear to be applicable, since typically a finitely generated abelian group will have infinitely many automorphisms. In this talk I will explain a theory of "commensurability" of groups, rings, and modules, developed in joint work with Hendrik Lenstra, which allows one to apply the above principle to a large class of modules over rings, including finitely generated Z[G]-modules, where G is a finite group (the title referring to the special case G={1}).

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