From the 1 of 11 linked papers with an AI index.
11 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…
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
The authors construct a torsion‑free supersoluble group of Hirsch length 14 with a normal series whose factors are all infinite cyclic, and they show that this group has a trivial…