7 citations · 14 across the 17 of their papers we have counts for
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Chain conditions on skew braces and solutions of the Yang-Baxter Equation
Massimiliano Di Matteo, Ramón Esteban-Romero, Maria Ferrara +1
Classical works of Hall and McLain show that solubility and local nilpotency play a key role in deriving finite generation in groups from maximal or minimal conditions on normal su…
Analogues of Grün's lemma and Baer's theorem for skew left braces
A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko +1
We prove in this paper some analogues of the well-known group-theoretical Grün's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem…
Representations of finite skew braces
A Ballester-Bolinches, R. Esteban-Romero, P. Pérez-Altarriba
One of the classical open problems in the theory of skew left braces is the study of their representation theory. We propose in this paper a definition of representation of a skew…
Addendum/Corrigendum to "On solubility of skew left braces and solutions of the Yang-Baxter equation"
A. Ballester-Bolinches, R. Esteban-Romero, P. Jiménez-Seral +1
In our previous work: Adv. Math. 455 (2024), no. 109880, solubility of solutions was introduced as an extension of solubility of skew braces in the classification context of non-de…
On left braces in which every subbrace is an ideal II
A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko +1
The aim of this paper is to take the study of Dedekind braces, that is, left braces for which every subbrace is an ideal, started in a previous paper, further. Dedekind braces …
On products of abelian skew braces
A. Ballester-Bolinches, R. Esteban-Romero, P. Pérez-Altarriba
The main objective of this paper is to study factorisations of skew left braces through abelian subbraces. We prove a skew brace theoretical analog of the classical Itô's theorem a…