7 citations · 9 across the 14 of their papers we have counts for
15 papers
Bisoluble and Binilpotent Skew Braces of Finite Morley Rank
Maria Ferrara, Moreno Invitti, Marco Trombetti +1
A connected skew brace of finite Morley rank is left nilpotent (resp. weakly soluble) whenever the additive and multiplicative groups are nilpotent (resp. are soluble and the left…
A probabilistic approach to the Yang--Baxter equation and skew braces
Maria Ferrara, Marco Trombetti, Cindy Tsang
We investigate finite non-degenerate set-theoretic solutions to the Yang--Baxter equation and skew braces using a probabilistic approach. We introduce four probabilities that measu…
A Counterexample to Byott's Conjecture for Finite Skew Braces
Massimiliano Di Matteo, Maria Ferrara, Marco Trombetti
We construct a finite skew brace with soluble additive group and insoluble multiplicative group. The multiplicative group has a quotient isomorphic to $\PSL_2(7)$, and hence the ex…
Finite-index Problems in Skew Braces
Massimiliano Di Matteo, Maria Ferrara
We investigate finite-index problems in skew braces. For every sub-skew brace \(A\) of a skew brace \(B\), we prove that finite additive index is equivalent to finite multiplicativ…
A Finite Skew Brace with Perfect Additive Group and Almost Simple Multiplicative Group
Massimiliano Di Matteo, Maria Ferrara
We construct a finite skew brace whose additive group is perfect and whose multiplicative group is non-perfect and almost simple. This gives an affirmative answer to Problem 20.109…
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 cardinalities whose arithmetical properties determine the structure of solutions of the Yang--Baxter equation
Maria Ferrara, Marco Trombetti, Cindy Tsang
The aim of this paper is to provide purely arithmetical characterisations of those natural numbers for which every non-degenerate set-theoretic solution of cardinality of t…
Skew Braces from a model-theoretic point of view 1
Maria Ferrara, Marco Trombetti, Moreno Invitti +1
Skew braces are one of the main algebraic tools controlling the structure of a non-degenerate bijective set-theoretic solution of the Yang-Baxter equation. The aim of this paper is…
On Dedekind Skew Braces
A. Caranti, I. Del Corso, M. Di Matteo +2
Skew braces play a central role in the theory of set-theoretic non-degenerate solutions of the Yang--Baxter equation, since their algebraic properties significantly affect the beha…
On the Sylow Theorem for Skew Braces
A. Caranti, I. Del Corso, M. Di Matteo +2
We discuss the (first) Sylow theorem for certain classes of finite skew braces, proving it to hold true when the skew brace is two-sided, bi-skew, right nilpotent, -homomorphic…
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…
Joins of -subnormal subgroups
Maria Ferrara, Marco Trombetti
Let be a partition of the set of all prime numbers. A subgroup of a finite group is~\textit{-subnormal} in if there exists a cha…
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…
On derived-indecomposable solutions of the Yang--Baxter equation
Ilaria Colazzo, Maria Ferrara, Marco Trombetti
If is a finite non-degenerate set-theoretic solution of the Yang--Baxter equation, the additive group of the structure skew brace is an -group, i.e. a group wh…