6 papers · 1 filter
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 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 …
On the structure of some one-generator nilpotent braces
Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. Subbotin
This article provides a detailed description of some nilpotent left braces generated by one element.
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…