Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-29T19:07:20.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Two maximal subgroups of a collineation group in five dimensions

Published online by Cambridge University Press:  24 October 2008

E. M. Hartley
E. M. Hartley
Affiliation:
Newnham CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Several recent papers have been concerned with a group G, of order 28.36.5.7, which can be represented as a collineation group in five dimensions. This collineation group is generated by harmonic inversions (projections) which leave fixed a point (the vertex) and a prime (said to be conjugate to the vertex). There are 126 projections in G and the set of 126 vertices form a configuration which is described in a paper (Hamill (3)) in which the operations of G are expressed as products of at most six projections. The group leaves invariant six algebraically independent primals; these have been determined (Todd (6)), and the equations of the simplest are given. The simplest invariant is a sextic primal, and some properties of this have been recorded in an earlier paper (Hartley (4)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 4 , October 1950 , pp. 555 - 569
Copyright
Copyright © Cambridge Philosophical Society 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Baker, H. F.A locus with 25920 linear self transformations (Cambridge, 1946).Google Scholar
(2)Dickson, L. E.Linear groups, with an exposition of the Galois field theory (Leipzig, 1901).Google Scholar
(3)Hamill, C. M.Proc. London Math. Soc. (in the Press).Google Scholar
(4)Hartley, E. M.Proc. Cambridge Phil. Soc. 46 (1950), 91–105.CrossRefGoogle Scholar
(5)Mitchell, H. H.American J. Math. 36 (1914), 1–12.CrossRefGoogle Scholar
(6)Todd, J. A.Proc. Cambridge Phil. Soc. 46 (1950), 73–90.CrossRefGoogle Scholar
(7)Todd, J. A.Proc. Roy. Soc. A, 200 (1950), 320–336.Google Scholar
(8)Veblen, O. and Maclagan-Wedderburn, J. H.Trans. American Math. Soc. 8 (1907), 387.Google Scholar