Probabilistically nilpotent groups

Shalev, Aner

doi:10.1090/proc/13867

Probabilistically nilpotent groups
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Proc. Amer. Math. Soc. 146 (2018), 1529-1536 Request permission

Abstract:

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 $\Gamma$ has a finite index subgroup which is nilpotent of class less than $k$.

Related results, generalizations and problems are also discussed.

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