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Probabilistically nilpotent groups


Author: Aner Shalev
Journal: Proc. Amer. Math. Soc. 146 (2018), 1529-1536
MSC (2010): Primary 20E26; Secondary 20P05
DOI: https://doi.org/10.1090/proc/13867
Published electronically: December 7, 2017
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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 $ 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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Additional Information

Aner Shalev
Affiliation: Einstein Institute of Mathematics Hebrew University Givat Ram, Jerusalem 91904 Israel
Email: shalev@math.huji.ac.il

DOI: https://doi.org/10.1090/proc/13867
Received by editor(s): June 8, 2017
Received by editor(s) in revised form: June 20, 2017
Published electronically: December 7, 2017
Additional Notes: The author was partially supported by ERC advanced grant 247034, ISF grant 1117/13 and the Vinik Chair of mathematics which he holds.
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2017 American Mathematical Society

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