Title: No iterated identities satisfied by all finite groups,
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 $w$. 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.