E. Ingrosso

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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

We give a negative solution to Problem~13.23 of the Kourovka Notebook. We construct a torsion-free group $G$ of Hirsch length $14$ admitting a finite series \[ 1=G_0\triangleleft G…