L. Childs has defined a skew brace (G,⋅,∘) to be a bi-skew brace if (G,∘,⋅) 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,⋅,∘) 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.

Bi-skew braces and regular subgroups of the holomorph / Caranti, A.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 562:(2020), pp. 647-665. [10.1016/j.jalgebra.2020.07.006]

Bi-skew braces and regular subgroups of the holomorph

Caranti A.
2020

Abstract

L. Childs has defined a skew brace (G,⋅,∘) to be a bi-skew brace if (G,∘,⋅) 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,⋅,∘) 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.
Caranti, A.
Bi-skew braces and regular subgroups of the holomorph / Caranti, A.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 562:(2020), pp. 647-665. [10.1016/j.jalgebra.2020.07.006]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/332734
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