首页|The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces

The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces

M. Ferrara M. Trombetti

来源：

Arxiv

The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces

M. Ferrara M. Trombetti

作者信息

Abstract

In this short note we establish the Schur--Zassenhaus Theorem and Sylow's Third Theorem for finite skew braces. More precisely, we prove that every Hall ideal of a finite skew brace admits a sub-skew brace complement, and more generally that every left ideal whose order is coprime to that of the Hall ideal can be embedded in such a complement. Using similar ideas we show that every left ideal of prime-power order is contained in a Sylow sub-skew brace. Finally, we prove that the number of Sylow $p$-sub-skew braces is congruent to $1$ modulo $p$, and provide examples showing that the corresponding containment property fails for arbitrary sub-skew braces.

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M. Ferrara,M. Trombetti.The Schur--Zassenhaus Theorem and Sylow's Third Theorem for Finite Skew Braces[EB/OL].(2026-06-30)[2026-07-03].https://arxiv.org/abs/2606.30453.

学科分类

数学

首发时间： 2026-06-30

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