Near-Rings and Skew Braces

Abstract

This paper provides a deeper analysis of Rump's correspondence between near-rings and skew braces. We show that, under a topological assumption on the structure of a near-ring, Rump's correspondence is invertible and it is always possible to construct an associated skew brace. Furthermore, we provide several examples where this topological assumption is fulfilled in well-known algebraic structures such as the Nottingham group, groups of triangular functions, iterated wreath products of arbitrary groups, and groups of IA-automorphisms of free nilpotent groups.