5 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 theore…
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…
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…
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…