Skew braces of size $p^2q$

TL;DR

This paper classifies and enumerates skew braces of size p^2q for odd primes p and q, providing explicit formulas especially for abelian types, based on subgroup classifications.

Contribution

It introduces a complete enumeration method for skew braces of size p^2q, including explicit formulas for abelian cases, advancing the understanding of their structure.

Findings

Explicit formulas for skew braces of abelian type.

Complete enumeration of skew braces of size p^2q.

Classification based on regular subgroups of holomorphs.

Abstract

In this paper we enumerate the skew braces of size $p^2q$ for $p,q$ odd primes by the classification of regular subgroups of the holomorph of the groups of size $p^2q$. In particular, we provide explicit formulas for the skew braces of abelian type.