Finite skew braces satisfy Schur-Zassenhaus for Hall ideals with complements and Sylow's third theorem on the count of Sylow p-sub-skew braces, with counterexamples for arbitrary sub-skew braces.
On finite trifactorised groups and Sylow and Hall theorems for skew braces
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The aim of this short note is to show that the Sylow theorem (respectively Hall theorem) for finite skew braces proved by Truman in arXiv:2606.18414 is a direct consequence of the Sylow structure (resp. Hall structure) of a finite trifactorised group. A Cauchy theorem for finite skew braces naturally emerges.
fields
math.GR 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves that in a finite skew brace B, any ideal I with |I| coprime to |B/I| admits a complement in B.
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The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces
Finite skew braces satisfy Schur-Zassenhaus for Hall ideals with complements and Sylow's third theorem on the count of Sylow p-sub-skew braces, with counterexamples for arbitrary sub-skew braces.
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A Schur--Zassenhaus Theorem for Finite Skew Braces
Proves that in a finite skew brace B, any ideal I with |I| coprime to |B/I| admits a complement in B.