Skew braces of size p2q II: Non-abelian type

Abstract

In this paper we enumerate the skew braces of non-abelian type of size p2q for p,q primes with q>2 by the classification of regular subgroups of the holomorph of the non-abelian groups of the same order. Since Crespo dealt with the case q=2, this paper completes the enumeration of skew braces of size p2q 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 V. Bardakov, M. Neshchadim and M. Yadav.