Journal Article10.2307/1968753
Discrete Groups Generated by Reflections
TL;DR: In this paper, a complete enumeration of the irreducible finite groups generated by reflections is given, along with a table with the number of reflections generated by two operations.
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Abstract: 1-3. Polytopes with restricted dihedral angles 590 4-7. Fundamental regions 594 8. The abstract definition 599 9. Complete enumeration of the irreducible groups 601 10-13. Continued products of the generators 602 14, 15. The central inversion 606 16. The total number of reflections 610 17. Generation by two operations 612 18. Elliptic space 617 Table of irreducible finite groups generated by reflections 618 Graphical representation 619 Index 620 References 620
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Citations
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Simple irreducible graded lie algebras of finite growth
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References
•Book
Theory of Groups of Finite Order
William Snow Burnside
- 01 Jan 1955
TL;DR: In this article, the authors define the notion of permutation groups as a group of linear substitutions, and show that a group can be represented as a permutation-group.
On the Orthogonal Groups in Four Dimensions
G. De B. Robinson,F. P. White +1 more
- 01 Jan 1931
TL;DR: In this paper, the authors classify the configurations of points lying on the hyper-sphere in [4] which may be said to possess the group property, and enumerate only those configurations which are essentially different from this point of view, in order to bring out any geometrical differences which might throw light on the fundamental problems of the theory of linear groups.
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