Proves Schur-Zassenhaus and Sylow theorems for finite skew braces: Hall ideals have complements, left ideals of prime-power order lie in Sylow sub-skew braces, and the number of Sylow p-sub-skew braces is congruent to 1 mod p.
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.
citing papers explorer
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The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces
Proves Schur-Zassenhaus and Sylow theorems for finite skew braces: Hall ideals have complements, left ideals of prime-power order lie in Sylow sub-skew braces, and the number of Sylow p-sub-skew braces is congruent to 1 mod p.
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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.