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.