Idealisation of Skew Left Braces
Sergio Camp-Mora, J. Pérez-Alemany, P. Pérez-Altarriba
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Source: Crossref
Published: Sep 1, 2026
DOI: 10.1007/s00009-026-03191-3
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Abstract Idealisation is the natural brace-theoretical analogue of normalisation in groups. Previous works have shown that idealisers do not exist for sub-skew braces in general. In this paper, we prove that they do exist for left ideals. We present a generalisation of the celebrated Frattini’s argument for skew left braces of nilpotent type. We also use this to introduce a Sylow system idealiser for nilpotent-type skew left braces, a generalisation of the Sylow system normaliser, and prove generalisations of some of its properties. Finally, we prove that the fixed ideals of a nilpotent-type skew left brace are contained in the hypercentre.
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