Topology & Geometric Group Theory Seminar

Fall 2011

1:30 – 2:30, Malott 203

Tuesday, October 25

Peter Kropholler, University of Glasgow (visiting Cornell)

Wilson's short proof of the Romanovskii-Wilson theorem

The theorem says this: let m and n be natural numbers with m < n. Suppose you have a group G which admits a presentation with n generators and m relators. Then for any set Y of generators of G, there is a subset of n-m elements of Y that freely generate a free group of rank n-m. It is proved by using ordered groups and embeddings in division rings to reduce it to the following statement about finite dimensional vector spaces: if V is an n-dimensional vector space and U is an m-dimensional subspace then any subset Y of of V which spans V modulo U contains a subset of n-m vectors which span a complement to U in V.

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