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arXiv · 2609.39430

Carter-like theorems for skew braces

Sergio Camp-Mora·J. Pérez-Alemany·P. Pérez-Altarriba
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Abstract

Analogues of the Sylow, Hall and Schur-Zassenhaus theorems for finite groups have recently been generalised to finite skew braces, providing a powerful framework for their structural analysis. Building on this foundation, the natural next step of skew braces is the study of Carter sub-skew braces, namely, centrally nilpotent, self-idealising sub-skew braces. However, while every finite soluble group possesses Carter subgroups, not every finite soluble skew brace possesses Carter sub-skew braces. We introduce Carter sub-skew braces, analyse their structural limitations and establish Carter-like theorems. We prove that finite soluble skew braces have Carter sub-skew braces if every sub-skew brace of prime-power order is a centrally nilpotent left ideal. We also prove their existence within finite multipermutational skew braces.

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Sergio Camp-Mora, J. Pérez-Alemany, P. Pérez-Altarriba. 2026-09-30. Carter-like theorems for skew braces. https://arxiv.org/abs/2609.39430

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