From the 2 of 10 linked papers with an AI index.
10 papers
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
The paper presents a construction of a finite skew brace whose additive group is perfect while its multiplicative group is non‑perfect and almost simple, answering a known problem…
Chain conditions on skew braces and solutions of the Yang-Baxter Equation
Massimiliano Di Matteo, Ramón Esteban-Romero, Maria Ferrara +1
The paper investigates how maximal and minimal chain conditions on ideals of skew braces relate to solubility and nilpotency, extending Hall‑McLain results, and introduces finitene…
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…