London Algebra Colloquium abstract
Bounding the residual finiteness of free groups
Martin Kassabov (Southampton), 24th February 2011
Abstract
We analyse the question of the minimal index of a normal subgroup in a
free group which does not contain a given element. Recent work by
Bou-Rabee–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.