Research Article
BibTex RIS Cite

On Algorithm Constructing Baer Subplanes of Hall plane

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

Elif Altıntaş Ayşe Bayar

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

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

Elif Altıntaş Ayşe Bayar

Abstract

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
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Elif Altıntaş

Ayşe Bayar

Publication Date October 15, 2021
Submission Date June 15, 2021
Acceptance Date October 5, 2021
Published in Issue Year 2021 Volume: 9 Issue: 2

Cite

APA Altıntaş, E., & Bayar, A. (2021). On Algorithm Constructing Baer Subplanes of Hall plane. Konuralp Journal of Mathematics, 9(2), 342-345.
AMA Altıntaş E, Bayar A. On Algorithm Constructing Baer Subplanes of Hall plane. Konuralp J. Math. October 2021;9(2):342-345.
Chicago Altıntaş, Elif, and Ayşe Bayar. “On Algorithm Constructing Baer Subplanes of Hall Plane”. Konuralp Journal of Mathematics 9, no. 2 (October 2021): 342-45.
EndNote Altıntaş E, Bayar A (October 1, 2021) On Algorithm Constructing Baer Subplanes of Hall plane. Konuralp Journal of Mathematics 9 2 342–345.
IEEE E. Altıntaş and A. Bayar, “On Algorithm Constructing Baer Subplanes of Hall plane”, Konuralp J. Math., vol. 9, no. 2, pp. 342–345, 2021.
ISNAD Altıntaş, Elif - Bayar, Ayşe. “On Algorithm Constructing Baer Subplanes of Hall Plane”. Konuralp Journal of Mathematics 9/2 (October 2021), 342-345.
JAMA Altıntaş E, Bayar A. On Algorithm Constructing Baer Subplanes of Hall plane. Konuralp J. Math. 2021;9:342–345.
MLA Altıntaş, Elif and Ayşe Bayar. “On Algorithm Constructing Baer Subplanes of Hall Plane”. Konuralp Journal of Mathematics, vol. 9, no. 2, 2021, pp. 342-5.
Vancouver Altıntaş E, Bayar A. On Algorithm Constructing Baer Subplanes of Hall plane. Konuralp J. Math. 2021;9(2):342-5.
 Download Cover Image
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.