English

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

Group Theory 2022-05-03 v3 Quantum Algebra Rings and Algebras

Abstract

In this paper we enumerate the skew braces of non-abelian type of size p2qp^2q for p,qp,q primes with q>2q>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=2q=2, this paper completes the enumeration of skew braces of size p2qp^2q 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.

Keywords

Cite

@article{arxiv.2004.04232,
  title  = {Skew braces of size $p^2q$ II: non-abelian type},
  author = {E. Acri and M. Bonatto},
  journal= {arXiv preprint arXiv:2004.04232},
  year   = {2022}
}

Comments

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 $p^2q$ of abelian type now included. v3: 43 pages, 20 tables, final version with significant improvements, to appear in Journal of Algebra and Its Applications