On Algorithm Constructing Baer Subplanes of Hall plane

Year 2021, Volume: 9 Issue: 2, 342 - 345, 15.10.2021

Elif Altıntaş , Ayşe Bayar

https://izlik.org/JA54XM53DX

Abstract

In this study, we construct an algorithm (implemented in C) to determine Baer subplanes of the projective plane of order 9 coordinatized by elements of a left nearfield of order 9 and classify these subplanes. Also, affine planes embedded in Baer subplanes are determined.

Keywords

Affine plane , projective plane , near field , baer subplane

References

• Z.Akca, S.Ekmekci and A.Bayar, On Fano Configurations of the Left Hall Plane of order 9, Konuralp journal of mathematics, 4, 2, 116-123, 2016.
• A.Bayar, Z.Akca, E. Altintas and S. Ekmekci. On the complete arcs containing the quadrangles constructing the Fano planes of the left near field plane of order 9. New Trends in Mathematical Science, 4(4), 266-266., 2016. 10.20852/ntmsci.2016.113 .
• R. H. Bruck, Difference Sets in a Finite Group, Trans, Amer. Math. Soc., 464-481, 1955.
• S. Ekmekci, A.Bayar, E. Altintas, Z.Akca, On the Complete (k,2)- Arcs of the Hall Plane of Order 9, International Journal of Advanced Research in Computer Science and Software Engineering, 6, 10, 282-288, 2016.
• M. Hall, The theory of groups , New York : Macmillan 1959.
• M. Hall, Jr. J.D. Swift and R. Killgrove, On projective planes of order nine, Math.Tables and Other Aids Comp. 13, 233-246, 1959.
• J.W.P. Hirschfeld, Projective geometries over finite fields, Second Edition, Clarendon Press, Oxford, 1998.
• J.W.P. Hirschfeld and J.A. Thas, General Galois Geometries, Springer Monographs in Mathematics, Springer- Verlag London 2016.
• T.G. Room - P.B. Kirkpatrick, Miniquaternion Geometry, London, Cambridge University Press, 177, 1971.
• O. Veblen and J.H.M. Wedderburn, Non-Desarguesian and non-Pascalian geometries, Trans. Amer. Math. Soc. 8, 379–388, 1907