Probabilistically nilpotent groups

Abstract

We show that, for a finitely generated residually finite group $\Gamma$, the word $[x_1,\dots ,x_k]$ is a probabilistic identity of $\Gamma$ if and only if $\Gamma$ is virtually nilpotent of class less than $k$. Related results, generalizations and problems are also discussed.

To appear in Proc. Amer. Math. Soc