## Topology & Geometric Group Theory Seminar

## Spring 2010

### 1:30 – 2:30, Malott 203

Tuesday, March 30

**Martin
Kassabov**, Cornell University

*Bounding the residual finiteness of free groups*

This is joint work with Francesco Matucci. We analyze the question of
the minimal index of a normal subgroup in a free group which does not
contain a given element. Recent work by BouRabee McReynolds and
Rivin give estimates for the index. By using results on the length of
shortest identities in finite simple groups we recover and improve
polynomial upper and lower bounds for the order of the quotient. The
bounds can be improved further if we assume that the element lies in
the lower central series.

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