6 citations · 16 across the 10 of their papers we have counts for
11 papers
Alternatives for pseudofinite groups
Abderezak Ould Houcine, Françoise Point
The famous Tits' alternative states that a linear group either contains a nonabelian free group or is soluble-by-(locally finite). We study in this paper similar alternatives in ps…
Ampleness in the free group
Abderezak Ould Houcine, Katrin Tent
We show that the theory of the free group -- and more generally the theory of any torsion-free hyperbolic group -- is -ample for any . We give also an explicit descript…
A remark on the definability of the Fitting subgroup and the soluble radical
A. Ould Houcine
Let be an arbitrary group. We show that if the Fitting subgroup of is nilpotent then it is definable. We show also that the class of groups whose Fitting subgroup is nilpot…
Finitely presented groups with infinitely many non-homeomorphic asymptotic cones
Denis Osin, Abderezak Ould Houcine
We construct a finitely presented group with infinitely many non-homeomorphic asymptotic cones. We also show that the existence of cut points in asymptotic cones of finitely presen…
Homogeneity and prime models in torsion-free hyperbolic groups
Abderezak Ould Houcine
We show that any nonabelian free group of finite rank is homogeneous; that is for any tuples , , having the same complete -type, there exists an auto…
The monomorphism problem in free groups
Laura Ciobanu, Abderezak Ould Houcine
Let be a free group of finite rank. We say that the monomorphism problem in is decidable if for any two elements and in , there is an algorithm that determines w…