Abstract
In both the Euclidean plane {mathbb {R}}^2 and the hyperbolic plane {mathbb {H}}^2, a non-trivial group of rotations has a unique fixed point. We compare groups of rotations of the three-dimensional spaces {mathbb {R}}^3 and {mathbb {H}}^3, and in each case we discuss the existence of a (possibly non-unique) common fixed point of the elements in such a group.
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