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The Abstract Group G3, 7, 16

Published online by Cambridge University Press:  20 January 2009

H. S. M. Coxeter
H. S. M. Coxeter
Affiliation:
Department of Mathematics, The University, Toronto
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A representation of degree 3 is used in § 4 to establish the necessary and sufficient condition

for the finiteness of the group (3, p | q, r) defined by

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 1 , June 1962 , pp. 47 - 61
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

REFERENCES

(1) Burnside, W., Theory of Groups of Finite Order (2nd ed., Cambridge University Press, 1911).Google Scholar
(2) Coxeter, H. S. M., Regular skew polyhedra in three and four dimensions, and their topological analogues, Proc. London Math. Soc., (2) 43 (1937), 34–62.Google Scholar
(3) Coxeter, H. S. M., The abstract groups Gm, n, p, Trans. Amer. Math. Soc., 45 (1939), 73–150.Google Scholar
(4) Coxeter, H. S. M., A method for proving certain abstract groups to be infinite, Bull. Amer. Math. Soc., 46 (1940), 246–251.CrossRefGoogle Scholar
(5) Coxeter, H. S. M., Integral Cayley numbers, Duke Math. J., 13 (1946), 561–578.CrossRefGoogle Scholar
(6) Coxeter, H. S. M., Regular polytopes (Methuen, London, 1948).Google Scholar
(7) Coxeter, H. S. M., The Real Projective Plane (2nd ed., Cambridge University Press, 1955).Google Scholar
(8) Coxeter, H. S. M., Groups generated by unitary reflections of period two, Canad. J. Math., 9 (1957), 243–272.CrossRefGoogle Scholar
(9) Coxeter, H. S. M., Introduction to Geometry (Wiley, New York, 1961).Google Scholar
(10) Coxeter, H. S. M. and Moser, W. O. J., Generators and Relations for Discrete Groups (Ergebnisse der Math. N.F. 14 (1957), Springer).CrossRefGoogle Scholar
(11) Edington, W. E., Abstract group definitions and applications, Trans. Amer. Math. Soc., 25 (1923), 193–210.CrossRefGoogle Scholar
(12) Klein, F., Ueber die Transformation siebenter Ordnung der elliptischen Functionen, Math. Ann., 14 (1879), 428–471.CrossRefGoogle Scholar
(13) Leech, J., Some definitions of Klein's simple group of order 168 and other groups, Proc. Glasgow Math. Assoc, 5 (1962), 166–175.CrossRefGoogle Scholar
(14) Leech, J. and Mennicke, J., Note on a conjecture of Coxeter, Proc. Glasgow Math. Assoc. 5 (1961), 25–29.CrossRefGoogle Scholar
(15) Miller, G. A., Groups generated by two operators of order three whose product is of order four, Bull. Amer. Math. Soc., 26 (1920), 361–369.CrossRefGoogle Scholar
(16) Sherk, F. A., The regular maps on a surface of genus three, Canad. J. Math., 11 (1959), 452–480.CrossRefGoogle Scholar
(17) Sinkov, A., On the group-defining relations (2, 3, 7; p), Ann. of Math., (2) 38 (1937), 577–584.CrossRefGoogle Scholar