A Schur--Zassenhaus Theorem for Finite Skew Braces

Abstract

We prove a Schur--Zassenhaus theorem for finite skew braces. More precisely, if \(B\) is a finite skew brace and \(I\) is an ideal of \(B\) such that \(|I|\) and \(|B/I|\) are coprime, then \(I\) admits a complement in \(B\).

6 pages. This version contains minor revisions and the addition of a short paragraph on supersolvable skew braces and the Lagrangian property. The main results and proofs remain unchanged