E. Ingrosso

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group extensions 1 Hirsch length 1 Kourovka Notebook problem 1 outer automorphism groups 1 supersoluble groups 1 torsion-free groups 1

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math.GR2026

On the independence of permutation characters

M. Brescia, E. Ingrosso, M. Trombetti

Let $G$ be a finite group. For every subgroup $H \leq G$ , let $π_{H}$ be the permutation character of the action of $G$ on the left cosets of $H$ . We prove that the characters $π_{H}$ ,…

math.GR2026

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 $A$ , we prove that \[ \widehat A \text{ is topologic…

math.GR2026

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…