Skew braces of size p2q II: Non-abelian type

Abstract

In this paper we enumerate the skew braces of non-abelian type of size [Formula: see text] for [Formula: see text] primes with [Formula: see text] by the classification of regular subgroups of the holomorph of the non-abelian groups of the same order. Since Crespo dealt with the case [Formula: see text], this paper completes the enumeration of skew braces of size [Formula: see text] started in a previous work by the authors. In some cases, we provide also a structural description of the skew braces. As an application, we prove a conjecture posed by Bardakov et al.