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Discrete parabolic groups. (English) Zbl 0793.53029
The main aim of the paper is to prove that any discrete group of isometries of a complete simply connected Riemannian manifold of pinched negative curvature, which fixes some point at infinity is finitely generated. As the main tool, the author uses Margulis Lemma which reduces the situation to nilpotent groups. This result is a step towards to proof that “geometrical finiteness” for such manifolds $$M$$ implies that $$\pi_ 1(M)$$ is finitely generated. For concept and criteria of geometrical finiteness for hyperbolic manifolds (of constant negative curvature), see B. N. Apanasov [Discrete groups in space and uniformization problems. Transl. from the Russian. Rev. and enlarged transl. (Dordrecht 1991; Zbl 0732.57001); for a review of the Russian original (1983; Zbl 0571.57002)].

##### MSC:
 53C10 $$G$$-structures 57S17 Finite transformation groups
##### Keywords:
group of isometries; pinched negative curvature
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