Skew Braces of Size p2 q I: Abelian Type

Abstract

This is the first part of a series of two articles. In this paper we enumerate and classify the left braces of size [Formula: see text], where[Formula: see text] and [Formula: see text] are distinct prime numbers, by the classification of regular subgroups of the holomorph of the abelian groups of the same order. We also provide the formulas that define the constructed braces.