Zobrazeno 1 - 10
of 1 181
pro vyhledávání: '"Ballester-Bolinches, A."'
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 Tsang can be improved and an answer to an open question set by Tsang a
Externí odkaz:
http://arxiv.org/abs/2405.14699
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 Dedekind left brace is centrally nilpotent. Structural results about D
Externí odkaz:
http://arxiv.org/abs/2405.04213
Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ \Pi $-property in $ G $ if there exists a $G$-chief series $ \varGamma_{G}: 1 =G_{0} < G_{1} < \cdot\cdot\cdot < G_{n}= G $ of $ G $ such that $ | G / G_{i-1}
Externí odkaz:
http://arxiv.org/abs/2404.01254
Autor:
Ballester-Bolinches, Adolfo, Esteban-Romero, Ramón, Ferrara, Maria, Pérez-Calabuig, Vicent, Trombetti, Marco
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 supersoluble skew braces have Sylow towers, and that in an arbitrary supersolubl
Externí odkaz:
http://arxiv.org/abs/2402.18486
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 $B$ of abelian type need not be right-nilpotent, but that this is the case if~$B$ is of nilpote
Externí odkaz:
http://arxiv.org/abs/2310.11123
Autor:
Ballester-Bolinches, Adolfo, Esteban-Romero, Ramón, Ferrara, Maria, Pérez-Calabuig, Vicent, Trombetti, Marco
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, we study their torsion theory (Section 4.1) and we introduce an "index"
Externí odkaz:
http://arxiv.org/abs/2310.07474
Autor:
Ballester-Bolinches, Adolfo, Esteban-Romero, Ramón, Jiménez-Seral, Paz, Pérez-Calabuig, Vicent
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 skew brace theoretical property of solubility is introduced and studied
Externí odkaz:
http://arxiv.org/abs/2304.13475
Autor:
Ballester-Bolinches, Adolfo, Esteban-Romero, Ramón, Kurdachenko, Leonid A., Pérez-Calabuig, Vicent
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 construction allows us to recover the construction of a free right nilpotent one
Externí odkaz:
http://arxiv.org/abs/2304.00532
We show that the number of isomorphism classes of left braces of order~$64$ with additive group isomorphic to $C_2\times C_2\times C_4\times C_4$ is $10\,326\,821$. This completes the classification of left braces of order~$64$, that turn out to fall
Externí odkaz:
http://arxiv.org/abs/2212.03167
Publikováno v:
Math. Comp., 93, no. 346, pp. 911-919, March 2024
We show that the number of isomorphism classes of left braces of order 64 with additive group isomorphic to $C_4 \times C_4 \times C_4$ is 1\,515\,429.
Comment: Math. Comp., in press
Comment: Math. Comp., in press
Externí odkaz:
http://arxiv.org/abs/2210.12823