Abstract
As the finite Hall planes are Non-Desarguesian, the Pappus Theorem does not hold in them. In this paper we state and prove some weaker versions of Pappus’s Theorem in Hall planes.
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Acknowledgements
This work was partially supported by the Simons Foundation Award ID: 426092 and the National Science Foundation Grant: 1855723. The authors are thankful to Eric Moorhouse for sharing his knowledge on Hall planes and, in particular, for correcting an error in the original description of the action of the collineation group on pairs of lines of the Hall plane. We are also thankful to Stefaan DeWinter, Bill Kantor, and Jason Williford for useful discussions on the topics of this paper. Finally, we are thankful to the anonymous referees for their useful comments, and, in particular, for suggesting the references [1, 20, 22].
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Communicated by Y. Zhou.
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Lazebnik, F., Leshock, L. On Pappus configurations in Hall planes. Des. Codes Cryptogr. 90, 1203–1219 (2022). https://doi.org/10.1007/s10623-022-01036-0
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DOI: https://doi.org/10.1007/s10623-022-01036-0