3 papers
math.GR2026
Non-split sharply 2- and 3-transitive groups in SL_n(\mathbb Z)
Marco Amelio, Simon André
We prove that contains a non-split sharply 2-transitive subgroup, answering a question of Glasner and Gulko. We also prove that $\mathrm{SL}_4(\mathbb{Z…
math.GR2026
Homogeneity in Coxeter groups and split crystallographic groups
Simon André, Gianluca Paolini
We prove that affine Coxeter groups, even hyperbolic Coxeter groups and one-ended hyperbolic Coxeter groups are homogeneous in the sense of model theory. More generally, we prove t…
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…