Aner Shalev
Published 2018-01-22Version 1
We show that, for a finitely generated residually finite group $\Gamma$, the word $[x_1, \ldots, x_k]$ 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.
Comments: To appear in Proc. Amer. Math. Soc
Probabilistically nilpotent groups of class two
A probabilistic Tits alternative and probabilistic identities
Obstruction to a Higman embedding theorem for residually finite groups with solvable word problem
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