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Discrete Groups of Motions

Published online by Cambridge University Press:  20 November 2018

Leon Greenberg
Leon Greenberg*
Affiliation:
Brown University
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This paper deals with the discrete groups of rigid motions of the hyperbolic plane. It is known (12) that the finitely generated, orientation-preserving groups have the following presentations:

Generators: .

Defining relations:

where km = ambmam-1bm-1. We shall denote this group by F(p; n1, … , nd; r).

In particular, the finitely generated free groups are contained among these. Indeed, one purpose of this paper is to indicate some geometrical methods for investigating free groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 415 - 426
Copyright
Copyright © Canadian Mathematical Society 1960

References

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