On $n$-isoclinism of skew braces

Abstract

Isoclinism was introduced by Hall and is an important concept in group theory. More generally, there is the notion of $n$-isoclinism for every natural number $n$. Recently, Letourmy and Vendramin (2023) extended the notions of isoclinism and also stem groups to the setting of skew braces. In this paper, we shall propose two analogs of $n$-isoclinism and $n$-stem groups for skew braces. We shall prove that for the ``weak" version, analogous to the case of groups, weak $n$-isoclinism implies weak $(n+1)$-isoclinism.

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