Skew braces of size $p^{2}q$ II: non-abelian type

Abstract

In this paper we enumerate the skew braces of non-abelian type of size $p^{2}q$ 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 $p^{2}q$ 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.

37 pages, 20 tables. We split a previous work arXiv:1912.11889 improving results and adding a treatment for the even case. v2: v2: arXiv identifier of our preprint on skew braces of size $p^{2}q$ of abelian type now included. v3: 43 pages, 20 tables, final version with significant improvements, to appear in Journal of Algebra and Its Applications

References in corpus (2)

• Hopf-Galois structures on extensions of degree $p^{2}q$ and skew braces of order $p^{2}q$: the cyclic Sylow $p$-subgroup case
• Skew braces of size $pq$

Cited by in corpus (1)

• Determining skew left braces of size np