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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…
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…
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…
Non-split sharply 2-transitive groups of odd positive characteristic
Marco Amelio, Simon André, Katrin Tent
It is well-known that every sharply 2-transitive group of characteristic 3 splits. Here we construct the first examples of non-split sharply 2-transitive groups in odd positive cha…
Finitely generated simple sharply 2-transitive groups
Simon André, Vincent Guirardel
We construct the first examples of infinite sharply 2-transitive groups which are finitely generated. Moreover, we construct such a group that has Kazhdan property (T), is simple,…