Abstract
We give sufficient conditions for a geometrically finite Kleinian group G acting in the hyperbolic space H n to have co-Hopf property, i.e., not to contain non-trivial proper subgroups isomorphic to itself. We provide examples of freely indecomposable geometrically finite non-elementary Kleinian groups which are not co-Hopf if our sufficient condition does not hold. We prove that any topologically tame non-elementary Kleinian group in dimension 3 can not be conjugate by an isometry to its proper subgroup.
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