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On a finite group of order 576

Published online by Cambridge University Press:  24 October 2008

C. M. Hamill
C. M. Hamill
Affiliation:
Newnham CollegeCambridge
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Bagnera(1) shows that when a certain primitive finite group of order 576, G576, is represented as a group of collineations in three-dimensional space, it contains twenty-four harmonic inversions with respect to points and planes, and he shows how to calculate the coordinates of the points and planes of the inversions. The purpose of this note is to discuss the configuration of these points, which we shall call vertices, to show that the whole group is generated by the twenty-four harmonic inversions, termed projections after Prof. Baker (2) and Dr J. A. Todd (4), and to enumerate the conjugate sets of the group.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 1 , January 1948 , pp. 26 - 36
Copyright
Copyright © Cambridge Philosophical Society 1948

References

REFERENCES

(1)Bagnera, G.R.C. Circ. Mat. Palermo, 19 (1905), 1–56.CrossRefGoogle Scholar
(2)Baker, H. F.A Locus with 25920 Linear Self-transformations (Cambridge, 1946).Google Scholar
(3)Hudson, R. W. H. T.Kummer's Quartic Surface (Cambridge, 1905).Google Scholar
(4)Todd, J. A.Proc. Roy. Soc. A, 189 (1947), 326–58.Google Scholar