Henry Bradford

University of Cambridge


Quantifying lawlessness in finitely generated groups


Algebra Seminar


25th November 2020, 2:30 pm – 3:30 pm
Online, Zoom


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".






Comments are closed.
css.php