Ty Ghaswala, Department of Pure Mathematics, University of Waterloo
“A Finite Group Walks Into a Bar...”
Last week, Rob seamlessly introduced the bar resolution, and showed us how we can view elements of Hn(G, A) as equivalence classes of set functions f : Gn → A satisfying a certain co-cycle condition. Miraculously, this was the last piece of machinery which needed to be built and this week we will use all of the heavy lifting we have done in the last 11 weeks or so to prove the following finite group theory result.
Let E be a group of order nm with n and m coprime. Then if E contains an abelian normal subgroup of order m, there exists a unique (up to conjugation) subgroup of order n.
This will complete the learning seminar for this term and there will be much rejoicing.
Please note room change.