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The Classification of Non-Euclidean Plane Crystallographic Groups

Published online by Cambridge University Press:  20 November 2018

A. M. Macbeath
A. M. Macbeath*
Affiliation:
University of Birmingham, Birmingham, England
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This paper deals with the algebraic classification of non-euclidean plane crystallographic groups (NEC groups, for short) with compact quotient space. The groups considered are the discrete groups of motions of the Lobatschewsky or hyperbolic plane, including those which contain orientation-reversing reflections and glide-reflections. The corresponding problem for Fuchsian groups, which contain only orientable transformations, is essentially solved in the work of Fricke and Klein (6).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1192 - 1205
Copyright
Copyright © Canadian Mathematical Society 1967

References

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