Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-29T16:09:21.223Z Has data issue: false hasContentIssue false

On the Clifford collineation, transform and similarity groups. I.

Published online by Cambridge University Press:  09 April 2009

Beverley Bolt
Affiliation:
University of Sydney.
T. G. Room
Affiliation:
University of Sydney.
G. E. Wall
Affiliation:
University of Sydney.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Papers I, II of this projected series lay the algebraic foundations of the theory of the Clifford groups; I deals with the case p > 2, II with the case p = 2. The present introduction refers to both papers. Our theory has applications in group theory, geometry and number theory.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1961

References

[1]Barnes, E. S. and Wall, G. E., Some extreme forms defined in terms of Abelian groups, This Journal I (1959), 4763.Google Scholar
[2]Bolt, Beverley, Ph.D. Thesis, Sydney University (1959).Google Scholar
[3]Dieudonné, J., La Géométrie des Groupes classiques (Springer, 1955).Google Scholar
[4]Horadam, A. F., A locus in [8] invariant under a group of order 51840 × 81, Quarterly J. Math. (2) 8 (1957), 241259.Google Scholar
[5]Horadam, A. F., Projection of an invariant locus in [8] from a solid lying on it, ibidem (2) 9 (1958), 8186.Google Scholar
[6]Horadam, A. F., Clifford groups in the plane, ibidem (2) 10 (1959), 294295.Google Scholar
[7]Horadam, A. F., Involutions associated with the Burkhardt configuration in [4], Canad. J. Math. 11 (1959), 1833.CrossRefGoogle Scholar
[8]Landau, E., Vorlesungen über Zahlentheorie, Bd. I (Leipzig, 1927).Google Scholar
[9]Morinaga, K. and Nono, T., On the linearization of a form of higher degree and its representation. J. Sci. Hiroshima Univ. A 16 (1952), 1341.Google Scholar
[10]Room, T. G., A synthesis of the Clifford matrices and its generalization, Amer. J. Math. 74 (1952), 967984.Google Scholar
[11]van der Waerden, B. L., Gruppen von linearen Transformationen (Springer, 1935; reprinted Chelsea, 1948).CrossRefGoogle Scholar