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A Note on Net Replacement in Transposed Spreads

Published online by Cambridge University Press:  20 November 2018

N. L. Johnson*
Affiliation:
Department of Mathematics, The University of IowaIowa City, IA 52242
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Abstract

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Let P be a translation plane containing a net N which is replaceable by . Let P' denote the transposed plane. We note that N' is replaceable by ()'. This result shows how to relate the various constructions of the two translation planes of order 16 that admit PSL(2, 7).

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Bruen, A., Spreads and a conjecture of Bruck and Bose, J. Algebra, Vol. 23, No. 3 (1972), pp. 519537.Google Scholar
2. Bruen, A. and Fisher, J.C., Spreads which are not dual spreads, Canad. Math. Bull. 12 (1969), pp. 801803.Google Scholar
3. Johnson, N.L., A note on the derived semifield planes of order 16, Aeq. Math. 18 (1978), pp. 103111.Google Scholar
4. Walker, M., A note on tangentially transitive affine planes, Bull. London Math. Soc. 8 (1976), pp. 273277.Google Scholar