5 citations · 13 across the 6 of their papers we have counts for
8 papers · 1 filter
Co-Hopfian virtually free groups and elementary equivalence
Simon André
We prove that two co-Hopfian finitely generated virtually free groups are elementarily equivalent if and only if they are isomorphic. We also prove that co-Hopfian finitely generat…
Simple sharply 2-transitive groups
Simon André, Katrin Tent
We construct simple sharply 2-transitive groups. Our result answers an open question of Peter Neumann. In fact, we prove that every sharply 2-transitive group of characteristic 0 e…
Formal solutions and the first-order theory of acylindrically hyperbolic groups
Simon André, Jonathan Fruchter
We generalise Merzlyakov's theorem about the first-order theory of non-abelian free groups to all acylindrically hyperbolic groups. As a corollary, we deduce that if is an acyl…
Acylindrical hyperbolicity and existential closedness
Simon André
Let be a finitely presented group, and let be a subgroup of . We prove that if is acylindrically hyperbolic and existentially closed in , then is acylindrical…
Elementary subgroups of virtually free groups
Simon André
We give a description of elementary subgroups (in the sense of first-order logic) of finitely generated virtually free groups. In particular, we recover the fact that elementary su…
On Tarski's problem for virtually free groups
Simon André
We give a complete classification of finitely generated virtually free groups up to -elementary equivalence. As a corollary, we give an algorithm that takes as inpu…
Virtually free groups are almost homogeneous
Simon André
Free groups are known to be homogeneous, meaning that finite tuples of elements which satisfy the same first-order properties are in the same orbit under the action of the automorp…
Hyperbolicity and Cubulability Are Preserved Under Elementary Equivalence
Simon André
The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and…