7 citations · 8 across the 6 of their papers we have counts for
7 papers
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…
On finite trifactorised groups and Sylow and Hall theorems for skew braces
A. Ballester-Bolinches, P. Pérez-Altarriba, V. Pérez-Calabuig
The aim of this short note is to show that the Sylow theorem (respectively Hall theorem) for finite skew braces proved by Truman in arXiv:2606.18414 is a direct consequence of the…
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…
Finite skew braces of square-free order and supersolubility
Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Maria Ferrara +2
The aim of this paper is to study supersoluble skew braces, a class of skew braces that encompasses all finite skew braces of square-free order. It turns out that finite supersolub…
Central nilpotency of left skew braces and solutions of the Yang-Baxter equation
Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Maria Ferrara +2
Nipotency of skew braces is related to certain types of solutions of the Yang-Baxter equation. This paper delves into the study of centrally nilpotent skew braces. In particular, w…
A note on right-nil and strong-nil skew braces
Adolfo Ballester-Bolinches, Maria Ferrara, Vicent Pérez-Calabuig +1
The aim of this short note is to completely answer Questions 2.34 and 2.35 of arXiv:1806.01127. In particular, we show that a finite strong-nil skew brace of abelian type need…