Probabilistically nilpotent groups

Aner Shalev

Probabilistically nilpotent groups

Group Theory 2018-01-23 v1

Authors: Aner Shalev

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.

Keywords

nilpotent groups group theory finite group theory

Cite

@article{arxiv.1801.07197,
  title  = {Probabilistically nilpotent groups},
  author = {Aner Shalev},
  journal= {arXiv preprint arXiv:1801.07197},
  year   = {2018}
}

Comments

To appear in Proc. Amer. Math. Soc

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