Abstract
It is proved that any relatively free associative Lie nilpotent algebra of a class \(l\) over a field of finite characteristic \(p\) satisfies the additive Frobenius relation \((a+b)^{p^s}=a^{p^s}+b^{p^s}\) if and only if \(l\le p^s-p^{s-1}+1\). It is also proved that, under the above conditions on the Lie class of nilpotency, the multiplicative Frobenius relation \((a\cdot b)^{p^s}=a^{p^s}\cdot b^{p^s}\) holds.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 417–422 https://doi.org/10.4213/mzm13637.
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Pchelintsev, S.V. Frobenius Relations for Associative Lie Nilpotent Algebras. Math Notes 113, 414–419 (2023). https://doi.org/10.1134/S0001434623030100
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DOI: https://doi.org/10.1134/S0001434623030100