7 citations · 14 across the 17 of their papers we have counts for
17 papers
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…
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…
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…
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.
Bounds on the number of maximal subgroups of finite groups
A. Ballester-Bolinches, R. Esteban-Romero, P. Jiménez-Seral
In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of rando…
Maximal subgroups of small index of finite almost simple groups
A. Ballester-Bolinches, R. Esteban-Romero, P. Jiménez-Seral
We prove in this paper that a finite almost simple group with socle the non-abelian simple group possesses a conjugacy class of core-free maximal subgroups whose index coin…