Skew braces of size $p^{2}q$

Abstract

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

We decided to withdraw this paper because we splitted our work into two parts extending and improving the results to cover all the skew braces of size $p^{2}q$ with $p$ and $q$ two different prime numbers. Therefore we completed the enumeration, including the even case that we avoided in this first work. The new versions are available at arXiv:2004.04291 and arXiv:2004.04232