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(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 language | English |
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Pages (from-to) | 167-197 |
Number of pages | 31 |
Journal | Israel Journal of Mathematics |
Volume | 233 |
Issue number | 1 |
DOIs | |
State | Published - 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.