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On the representation of the modular group of order ½p (p2 – 1) as a group of linear substitutions on ½ (p – 1) symbols, ichen p is a prime of the form 4n + 3

Published online by Cambridge University Press:  24 October 2008

W. Burnside
W. Burnside
Affiliation:
Honorary Fellow of Pembroke College.
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Extract

The actual form of the set of linear substitutions on 3 symbols, which gives a representation of the simple group of order 168, has been known for many years.

In these Proceedings (vol. 20, pp. 247–9) I have determined the form of the set of linear substitutions on 5 symbols which gives a representation of the simple group of order 660.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 5 , July 1925 , pp. 779 - 787
Copyright
Copyright © Cambridge Philosophical Society 1925

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References

* It is given, for instance, in Klein's, Vorlesungen über die Theorie der ellip-tiscken Modulfunctionen, vol. 1, p. 705Google Scholar; and in Weber's, Lehrbuch der Algebra, vol. 2, § 131Google Scholar. See also Burnside, , Theory of Groups, 2nd edition, p. 311.Google Scholar

† Burnside, , Theory of Groups, p. 436.Google Scholar

* loc. cit. p. 502.Google Scholar

* Burnside, , Proc. Land. Math. Soc. vol. 3 (second series), p. 246.Google Scholar