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A uniformly quasiconformal group not isomorphic to a Möbius group. (Russian, English) Zbl 1079.30023

Sib. Mat. Zh. 45, No. 5, 1032-1038 (2004); translation in Sib. Math. J. 45, No. 5, 849-854 (2004).
The paper under review is concerned with the question of how much the class of uniformly quasiconformal groups is broader than the class of Möbius groups. On the base of the results of M. Eh. Kapovich [Sib. Math. J. 30, No. 5, 712–722 (1989; Zbl 0694.53029)] and N. A. Isachenko [Sov. Math. Dokl., 42, No. 1, 125–128 (1991; Zbl 0741.57010)], the author constructs a uniformly quasiconformal group which is not isomorphic to any Möbius group. A presentation of the group is given.

MSC:

30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
57S25 Groups acting on specific manifolds
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