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On Algorithm Constructing Baer Subplanes of Hall plane

Yıl 2021, Cilt: 9 Sayı: 2, 342 - 345, 15.10.2021

Öz

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.

Kaynakça

  • 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
Yıl 2021, Cilt: 9 Sayı: 2, 342 - 345, 15.10.2021

Öz

Kaynakça

  • 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
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Elif Altıntaş

Ayşe Bayar

Yayımlanma Tarihi 15 Ekim 2021
Gönderilme Tarihi 15 Haziran 2021
Kabul Tarihi 5 Ekim 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 2

Kaynak Göster

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. Ekim 2021;9(2):342-345.
Chicago Altıntaş, Elif, ve Ayşe Bayar. “On Algorithm Constructing Baer Subplanes of Hall Plane”. Konuralp Journal of Mathematics 9, sy. 2 (Ekim 2021): 342-45.
EndNote Altıntaş E, Bayar A (01 Ekim 2021) On Algorithm Constructing Baer Subplanes of Hall plane. Konuralp Journal of Mathematics 9 2 342–345.
IEEE E. Altıntaş ve A. Bayar, “On Algorithm Constructing Baer Subplanes of Hall plane”, Konuralp J. Math., c. 9, sy. 2, ss. 342–345, 2021.
ISNAD Altıntaş, Elif - Bayar, Ayşe. “On Algorithm Constructing Baer Subplanes of Hall Plane”. Konuralp Journal of Mathematics 9/2 (Ekim 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 ve Ayşe Bayar. “On Algorithm Constructing Baer Subplanes of Hall Plane”. Konuralp Journal of Mathematics, c. 9, sy. 2, 2021, ss. 342-5.
Vancouver Altıntaş E, Bayar A. On Algorithm Constructing Baer Subplanes of Hall plane. Konuralp J. Math. 2021;9(2):342-5.
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