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Derivable Nets1)

Published online by Cambridge University Press:  20 November 2018

T. G. Ostrom
T. G. Ostrom*
Affiliation:
Washington State University
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Up to a duality, the known finite projective planes which are not translation planes all are equivalent to affine planes which contain the type of structure defined below to be a "derivable net". (Insofar as the known finite planes are concerned, this means that the intimate connection between projective geometry and linear algebra still holds for non-Desarguesian planes.)

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 5 , October 1965 , pp. 601 - 613
Copyright
Copyright © Canadian Mathematical Society 1965

Footnotes

1)

This work was supported (in part) by grant No. GP 1623 from the National Science Foundation.

References

1. Andre', J., Űber nicht-Desarguessche Ebenen mit Transitiver Translationsgruppe. Math. Z. 60 (1954), 156-186.Google Scholar
2. Bruck, R.H., Existence Problems for Classes of Finite Planes. Mimeographed notes of lectures delivered to the Canadian Mathematics Seminar, meeting in Saskatoon, Sask., August, 1963.Google Scholar
3. Bruck, R.H. and Bose, R. C., The Construction of Translation Planes from Projective Spaces. J. Alg. 1 (1964), 85-102.Google Scholar
4. Ostrom, T.G., Semi-translation Planes. Trans. Am. Math. Soc. 111 (1964), 1-18.Google Scholar