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arXiv · 1801.07197

Probabilistically nilpotent groups

Aner Shalev
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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 $\Gamma$ is virtually nilpotent of class less than $k$. Related results, generalizations and problems are also discussed.

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Aner Shalev. 2018-01-22. Probabilistically nilpotent groups. https://arxiv.org/abs/1801.07197

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