[Binghamton Geometry/Topology Seminar] Oct 13

[Dmytro Savchuk]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, Oct 13, 2011
*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson Reading
Room.

*Speaker:* Peter Kropholler* *(University of Glasgow)
*Title:* Wilson's short proof of the Romanovskii-Wilson Theorem* *
*
Abstract:*  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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