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19.32 (2018)

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Let $p \geqslant 673$ be a prime and $r \geqslant 2$ be an integer. Let $B$ be the free group in the Burnside variety of exponent $p$ on $a_1, \dots, a_r$. Must every non-identical one-variable equation $w(a_1, \dots, a_r, x) = 1$ over $B$ have at most finitely many solutions in $B$?

Contributor: A. Gaglione

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