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$z$-classes of isometries of the hyperbolic space. (English) Zbl 1206.51017
The results concerning the given problem reflected in the title are formulated in four main theorems. These theorems are firstly presented in introduction and then proved by means of several technical statements. Some more explicit simple criteria are presented separately in the last section. Further technical calculations are supplied in two appendices.
##### MSC:
 51M10 Hyperbolic and elliptic geometries (general) and generalizations 51F25 Orthogonal and unitary groups (geometry)