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arXiv · 2606.26286

Analogues of Gr\"un's lemma and Baer's theorem for skew left braces

A. Ballester-Bolinches·R. Esteban-Romero·L. A. Kurdachenko·P. Pérez-Altarriba
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Abstract

We prove in this paper some analogues of the well-known group-theoretical Gr\"un's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem, stating that if the quotient by the nth centre of a group is finite, then so is the $(n + 1)$th term of the lower central series, in the scope of nfinite slew left braces. These results represent significant improvements over previous work. The trifactorised group associated with a skew left brace will be crucial for our proofs.

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A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko, P. Pérez-Altarriba. 2026-06-24. Analogues of Gr\"un's lemma and Baer's theorem for skew left braces. https://arxiv.org/abs/2606.26286

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