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math.GR2026
Realizing Non-Archimedean Polish Groups as Outer Automorphism Groups
Gianluca Paolini, Jean-Luc Rabideau
We prove that every non-Archimedean Polish group is topologically isomorphic to the outer automorphism group of a countable discrete group. Furthermore, our construction is Borel.…
math.GR2025
On the existence of uncountable Hopfian and co-Hopfian abelian groups
Gianluca Paolini, Saharon Shelah
We deal with the problem of existence of uncountable co-Hopfian abelian groups and (absolute) Hopfian abelian groups. Firstly, we prove that there are no co-Hopfian reduced abelian…
math.GR2025
Around first-order rigidity of Coxeter groups
Simon André, Gianluca Paolini
By the work of Sela, for any free group , the Coxeter group is elementarily equivalent to…