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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
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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

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References

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