7 citations · 12 across the 18 of their papers we have counts for
21 papers
The group class SJ is not countably recognizable
M. Brescia, B. G. Di Siena, E. Ingrosso +1
A group is an {\it $\SJ$-group} if it admits a general abelian series all of whose terms are subnormal of finite defect in the whole group. We construct a group which is not an…
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…
Relative commuting probability and BFC-type results for finite skew braces
Susanta Mondal, Pavel Shumyatsky, Marco Trombetti +1
We develop a probabilistic approach to the structure of finite skew left braces, motivated both by classical commuting probability in finite group theory and by the role of skew le…
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…
On the independence of permutation characters
M. Brescia, E. Ingrosso, M. Trombetti
Let be a finite group. For every subgroup , let be the permutation character of the action of on the left cosets of . We prove that the characters ,…
A torsion-free group of nilpotency class six with all subgroups subnormal of defect at most
Mattia Brescia, Bernardo Giuseppe Di Siena, Marco Trombetti
Casolo asked whether a torsion-free group in which every subgroup is subnormal of defect at most must be nilpotent of class at most . The answer is known to be positive for…
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…
Hopficity of profinite completions of abelian groups
M. Brescia, E. Ingrosso, M. Trombetti
We determine exactly when the profinite completion of an arbitrary abelian group is topologically Hopfian. For an abelian group , we prove that \[ \widehat A \text{ is topologic…
A Torsion-free Supersoluble Group with Trivial Outer Automorphism Group
Mattia Brescia, Ernesto Ingrosso, Marco Trombetti
We give a negative solution to Problem~13.23 of the Kourovka Notebook. We construct a torsion-free group of Hirsch length admitting a finite series \[ 1=G_0\triangleleft G…
Finite groups with a large normalized sum of element orders
Luigi Iorio, Marco Trombetti
For a finite group , let be the sum of the orders of its elements, and define the corresponding normalized sum as , where $\mathcal{C}…
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 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…
On the lattice of closed subgroups of a profinite group
Francesco de Giovanni, Iker de las Heras, Marco Trombetti
The subgroup lattice of a group is a great source of information about the structure of the group itself. The aim of this paper is to use a similar tool for studying profinite grou…
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…
The structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented
Marco Trombetti
The aim of this paper is to show that the structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented.
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…
A note on the series' of ordinal numbers
Marco Trombetti
The aim of this short note is to provide a proof to a statement of Sierpiński concerning the number of possible sums of a series (of type ) of arbitrary ordinal numbers…