No iterated identities satisfied by all finite groups

Alexei Belov, Anna Erschler

Research output: Contribution to journalArticlepeer-review


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(lC) 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 languageEnglish
Pages (from-to)167-197
Number of pages31
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Aug 2019

Bibliographical note

Funding Information:
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.

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


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