Isoclinism of skew braces

Abstract

We define isoclinism of skew braces and present several applications. We study some properties of skew braces that are invariant under isoclinism. For example, we prove that right nilpotency is an isoclinism invariant. This result has application in the theory of set-theoretic solutions to the Yang-Baxter equation. We define isoclinic solutions and study multipermutation solutions under isoclinism.

arXiv comment14 pages. Postprint version

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Cited by in corpus (6)

• Relative Rota-Baxter groups and skew left braces
• Schur covers of skew braces
• Schur multiplier and Schur covers of relative Rota-Baxter groups
• On Grün's lemma for perfect skew braces
• A classification of module braces over the ring of $\mathbf{p}$-adic integers
• Common divisor graphs for skew braces