Bi-skew braces and regular subgroups of the holomorph

[摘要] L. Childs has defined a skew brace (G, ., o) to be a biskew brace if (G, o, .) is also a skew brace, and has given applications of this concept to the equivalent theory of Hopf-Galois structures. The goal of this paper is to deal with bi-skew braces (G, ., o) from the yet equivalent point of view of regular subgroups of the holomorph of (G, .). In particular, we find that certain groups studied by T. Kohl, F. Dalla Volta and the author, and C. Tsang all yield examples of bi-skew braces. Building on a construction of Childs, we also give various methods for exhibiting further examples of bi-skew braces. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Holomorph;Multiple holomorph;Skew braces;Bi-skew braces;Regular subgroups;Automorphisms