7 citations · 12 across the 18 of their papers we have counts for
10 papers · 1 filter
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}…