Skew braces of size $p^{2}q$ I: abelian type

Abstract

This is the first part of a series of two articles. In this paper we enumerate and classify the left braces of size $p^{2}q$ where $p$ and $q$ are distinct prime numbers by the classification of regular subgroups of the holomorph of the abelian groups of the same order. We also provide the formulas that define the constructed braces.

21 pages, 21 tables. We split a previous work arXiv:1912.11889 improving results and adding a treatment for the even case. v2: arXiv identifier of our preprint on skew braces of size $p^{2}q$ of non-abelian type now included. v3: final version

References in corpus (5)

• Semigroups of I-type
• Hopf-Galois structures on extensions of degree $p^{2}q$ and skew braces of order $p^{2}q$: the cyclic Sylow $p$-subgroup case
• Bi-skew braces and Hopf Galois structures
• Hopf Galois structures on extensions of degree twice an odd prime square and their associated left braces
• Automorphism groups of groups of order $p^2{q}^2$

Cited by in corpus (2)

• Enumeration of left braces with additive group $C_4\times C_4\times C_4$
• Determining skew left braces of size np