Henry Bradford (Cambridge), `Quantifying lawlessness for finitely generated groups'

Abstract: A group is lawless if no non-trivial word map vanishes on it. We introduce a function which measures the difficulty of verifying the non-vanishing of word maps on a finitely generated lawless group. We characterize groups for which this function is bounded; construct examples where it grows slowly and quickly, and give some modest bounds for Grigorchuk's group and Thompson's group F. Finally we note a connection with the quantitative version of residual finiteness due to Bou-Rabee.