Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-11T13:02:39.849Z Has data issue: false hasContentIssue false
  • English
  • Français

A characterization of generalized Hall planes

Published online by Cambridge University Press:  17 April 2009

N.L. Johnson
N.L. Johnson
Affiliation:
The University of Iowa, Iowa City, Iowa, USA.
Rights & Permissions [Opens in a new window]

Abstract

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.

We prove that a translation plane π of odd order is a generalized Hall plane if and only if π is derived from a translation plane of semi-translation class 1–3a. Also, a derivable translation plane of even order and class 1–3a derives a generalized Hall plane. We also show that the generalized Hall planes of Kirkpatrick form a subclass of the class of planes derived from the Dickson semifield planes.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 61 - 67
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Albert, A.A., “The finite planes of Ostrom”, Bol. Soc. Mat. Mexicans (2) 11 (1966), 1–13.Google Scholar
[2]Hall, Marshall Jr, The theory of groups (The Macmillan Company, New York, 1959).Google Scholar
[3]Johnson, Norman Lloyd, “A classification of semi-translation planes”, Canad. J. Math. 21 (1969), 1372–1387.CrossRefGoogle Scholar
[4]Johnson, Norman L., “Derivable semi-translation planes”, Pacific J. Math. 34 (1970), 687–707.Google Scholar
[5]Johnson, Norman L., “Translation planes constructed from semifield planes”, Pacifia J. Math. 36 (1971 ), 701–711.CrossRefGoogle Scholar
[6]Kirkpatrick, P.B., “Generalization of Hall planes of odd order”, Bull Austral. Math. Soc. 4 (1971), 205–209.Google Scholar
[7]Ostrom, T.G., “Semi-translation planes”, Trans. Amer. Math. Soc. 111 (1964), 1–18.Google Scholar
[8]Ostrom, T.G., “Vector spaces and construction of finite projective planes”, Arch. Math. 19 (1968), 1–25.Google Scholar