Some properties of skew braces that are invariant under isoclinism

TL;DR

This paper investigates properties of skew braces that remain unchanged under isoclinism, a concept recently introduced, highlighting invariance of certain algebraic properties.

Contribution

It demonstrates that bi-skew, λ-homomorphic, and inner properties of skew braces are invariant under isoclinism.

Findings

Bi-skew property is invariant under isoclinism

λ-homomorphic property is invariant under isoclinism

Inner property is invariant under isoclinism

Abstract

Letourmy and Vendramin have recently introduced a concept of isoclinism for skew braces. We show that for a skew brace the properties of being bi-skew, $\lambda$-homomorphic, and inner are invariant under isoclinism.