Quantifying lawlessness in finitely generated groups
25th November 2020, 2:30 pm – 3:30 pm
A group is lawless if no non-trivial word map vanishes on it. We introduce a "lawlessness growth" function which measures the difficulty of verifying the non-vanishing of word maps on a finitely generated lawless group. We characterize groups on bounded lawlessness growth; construct examples of both slow and fast lawlessness growth, and give some bounds for Grigorchuk's group and Thompson's group F. We note a connection with the quantitative version of residual finiteness due to Bou-Rabee. Time permitting, we will note some ways in which the behaviour of the growth function changes if "word maps" are replaced in the definition by "word maps with constants".