1,128 research outputs found
Homogeneity and prime models in torsion-free hyperbolic groups
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 automorphism of which sends to .
We further study existential types and we show that for any tuples , if and have the same existential -type,
then either has the same existential type as a power of a primitive
element, or there exists an existentially closed subgroup (resp.
) of containing (resp. ) and an isomorphism
with .
We will deal with non-free two-generated torsion-free hyperbolic groups and
we show that they are -homogeneous and prime. This gives, in
particular, concrete examples of finitely generated groups which are prime and
not QFA
Exact solutions of scalar bosons in the presence of the Aharonov-Bohm and Coulomb potentials in the gravitational field of topological defects
In this paper, we analyzed the relativistic quantum motion of a charged
scalar particles in the presence of a Aharonov Bohm and Coulomb potentials in
the spacetimes produced by an idealized cosmic strings and global monopoles.Comment: any comments are welcom
Ampleness in the free group
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 description of the imaginary algebraic closure in free groups
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