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On the Clifford collineation, transform and similarity groups. (III) Generators and involutions

Published online by Cambridge University Press:  09 April 2009

Beverley Bolt
Beverley Bolt
Affiliation:
Coulmbia University, New York, U.S.A. The University of Sydney, Sydney, Australia.
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In this paper the Clifford groups PCT(pm), p > 2, PCG(pm) and CS'(pm), and the factor groups ½CS' (pm), which were defined in Paper I of this series (Bolt, Room and Wall [1]), are considered as transformations of projective [pm–1] over the complex field, C. We note that the geometrical results are the same if any of the corresponding groups CT, CG or GG and CS, respectively, are considered instead.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 3 , February 1962 , pp. 334 - 344
Copyright
Copyright © Australian Mathematical Society 1962

References

[1]Bolt, Beverley, Room, T. G. and Wall, G. E., On the Clifford Collineation, Transform and Similarity Groups I, This Journal 2 (1961). 60–79.Google Scholar
[2]Bolt, Beverley, Room, T. G. and Wall, G. E., On the Clifford Collineation, Transform and Similarity Groups II, Journal, 80–96.Google Scholar
[3]Dickson, L. E., Linear Groups with an Exposition of the Galois Field Theory (Leipzig, 1901).Google Scholar
[4]Dieudonné, J., La Géométrie des Groupes Classiques (Berlin, 1955), Ergebnisse der Mathematik, (N.F.) 5.Google Scholar
[5]Horadam, A. F., Quart. J. Math. (Oxford 2nd Series) 8 (1957), 241–259.CrossRefGoogle Scholar
[6]Horadam, A. F., Canadian J. Math. 11 (1959) 18–33.CrossRefGoogle Scholar
[7]Room, T. G. and Smith, R. J., Quart. J. Math. (Oxford 2nd Series) 9 (1958), 177–182.CrossRefGoogle Scholar
[8]Todd, J. A., Analytical and Projective Geometry (London, 1947) 172.Google Scholar
[9]Todd, J. A., Proc. Camb. Phil. Soc. 46 (1950), 73–90.CrossRefGoogle Scholar