No iterated identities satisfied by all finite groups

Alexei Belov; Anna Erschler

doi:10.1007/s11856-019-1904-4

No iterated identities satisfied by all finite groups

Alexei Belov, Anna Erschler

Department of Mathematics

École normale supérieure

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that there is no iterated identity satisfied by all finite groups. For w being a non-trivial word of length l, we show that there exists a finite group G of cardinality at most exp(l^C) which does not satisfy the iterated identity w. We also prove a more general statement concerning iterations of an endomorphism of a free group. The proof uses the approach of Borisov and Sapir, who used dynamics of polynomial mappings for the proof of non-residual finiteness of some groups.

Original language	English
Pages (from-to)	167-197
Number of pages	31
Journal	Israel Journal of Mathematics
Volume	233
Issue number	1
DOIs	https://doi.org/10.1007/s11856-019-1904-4
State	Published - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, The Hebrew University of Jerusalem.

Funding

The work of the authors is partially supported by the ERC grant GroIsRan. This work of the first-named author is also supported by the Russian Science Foundation grant No. 17-11-01377.

Funders	Funder number
Horizon 2020 Framework Programme	725773
European Commission
Russian Science Foundation	17-11-01377

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10.1007/s11856-019-1904-4

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No iterated identities satisfied by all finite groups

Abstract

Bibliographical note

Funding

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