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arXiv · 2609.35396

Grün's Lemma for Semiassociative Mal'cev Algebras

Alexander Wires
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Abstract

We extend recent work on analogues of Grün's Lemma from skew-braces to all semiassociative Mal'cev algebras which is a broad class of algebras encompassing all expansions of groups. The direct analogue of Grün's Lemma is known to fail for skew-braces; thus, the more general result is a characterization for perfect algebras of when the upper-central series stabilizes at the second-center. The proof is an application of the description of generating sets for commutators in Mal'cev algebras.

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Alexander Wires. 2026-09-28. Grün's Lemma for Semiassociative Mal'cev Algebras. https://arxiv.org/abs/2609.35396

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