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Discrete extensions of Lannér groups. (English. Russian original) Zbl 0960.20030
Dokl. Math. 58, No. 1, 78-80 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 361, No. 4, 439-442 (1998).
From the introduction: In F. Lannér’s work [Meddel. Lunds Univ. Mat. Semin. 11 (1950; Zbl 0037.39802)], all tetrahedra in the hyperbolic space $$H^3$$ whose dihedral angles are integers submultiples of $$\pi$$ are found. Starting with works by E. B. Vinberg and by L. A. Best, reflection groups in the faces of Lannér tetrahedra and their subgroups of finite index attract attention of mathematicians specializing in discrete groups. In this paper, we prove that all discrete extensions of the groups mentioned in the complete isometry group $$\text{Is}(H^3)$$ of hyperbolic space are normal and give their complete description.

##### MSC:
 20H15 Other geometric groups, including crystallographic groups 20E07 Subgroup theorems; subgroup growth