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21.63 (2026)

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(E. Zelmanov). Let $F$ be a field of characteristic $p > 0$, and let $\Gamma$ be the principal congruence subgroup of $\text{Aut}(F[x_1, \dots, x_n])$ consisting of all automorphisms that send each variable $x_i$ to $x_i$ modulo terms of higher degree. Then $\Gamma$ is a residually $p$ group. Does $\Gamma$ satisfy a pro-$p$ identity?

Contributor: E. I. Khukhro

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