Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Universitat Politècnica de València, Universitat de València
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215069059