<br><div class="gmail_quote"><div class="gmail_quote"> BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR<br><div class="gmail_quote"><div class="gmail_quote"><div class="gmail_quote"><div class="gmail_quote"><div class="gmail_quote">
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<br><i>Date:</i> Thursday, Oct 13, 2011<br>
<i>Time:</i> 2:50-3:50pm<br><i>Place:</i> Library North 2205 followed by coffee/tea in the Anderson Reading Room.<br>
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<i>Speaker:</i> Peter Kropholler<b> </b>(University of Glasgow)<br><i>Title:</i> Wilson's short proof of the Romanovskii-Wilson Theorem<em> </em><div>
<i><br>Abstract:</i> 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.</div><em> <br></em></div></div></div></div></div></div></div></div></div><br>
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