7 citations · 15 across the 16 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…
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…
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 finitely generated left nilpotent braces
H. Meng, A. Ballester-Bolinches, L. A. Kurdachenko +1
A description of finitely generated left nilpotent braces of class at most two is presented in this paper. The description heavily depends on the fact that if is left nilpotent…
On left nilpotent skew braces of class 2
A. Ballester-Bolinches, L. A. Kurdachenko, V. Pérez-Calabuig
The main objective of this article is to initiate a detailed structure theory of left nilpotent skew braces of class , i.e. skew braces with . We prove that if …
Categories of skew left braces and trifactorised groups
A. Ballester-Bolinches, R. Esteban-Romero, P. Pérez-Altarriba +1
The main objective of this paper is to deepen the relationship between skew left braces and trifactorised groups that encodes the information about skew left braces, their structur…
Constructing skew left braces whose additive group has trivial centre
A. Ballester-Bolinches, R. Esteban-Romero, P. Jiménez-Seral +1
A complete description of all possible multiplicative groups of finite skew left braces whose additive group has trivial centre is shown. As a consequence, some earlier results of…
On left braces in which every subbrace is an ideal
A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko +1
The aim of this paper is to introduce and study the class of all left braces in which every subbrace is an ideal. We call them Dedekind left braces. It is proved that every finite…
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…
Soluble skew left braces and soluble solutions of the Yang-Baxter equation
Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Paz Jiménez-Seral +1
The study of non-degenerate set-theoretic solutions of the Yang-Baxter equation calls for a deep understanding of the algebraic structure of a skew left brace. In this paper, the s…
From actions of an abelian group on itself to left braces
Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Leonid A. Kurdachenko +1
We present a construction of left braces of right nilpotency class at most two based on suitable actions of an abelian group on itself with an invariance condition. This constructi…
Set-theoretical solutions of the pentagon equation on Clifford semigroups
Marzia Mazzotta, Vicent Pérez-Calabuig, Paola Stefanelli
Given a set-theoretical solution of the pentagon equation on a set and writing , with a binary operation on …
Enumeration of left braces with additive group
A. Ballester-Bolinches, R. Esteban-Romero, V. Pérez-Calabuig
We show that the number of isomorphism classes of left braces of order~ with additive group isomorphic to is . This completes…
Enumeration of left braces with additive group
A. Ballester-Bolinches, R. Esteban-Romero, V. Pérez-Calabuig
We show that the number of isomorphism classes of left braces of order 64 with additive group isomorphic to is 1\,515\,429.