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SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE

Year 2023, Volume: 11 Issue: 2, 143 - 147, 28.08.2023

Ziya Akça

https://doi.org/10.20290/estubtdb.1302633

Abstract

En küçük Kartezyen grubunun elemanlarıyla koordinatlanan 25. mertebeden bir projektif düzlem π olsun. Bu çalışmada, düzgün dörtgenin seçimine bağlı olarak bazı durumlarda π nin 3. mertebeden herhangi bir projektif alt düzlemi olmadığı gösterilmektedir.

Keywords

Kartezyen grup Projektif Düzlem Cebirsel yapı

References

  • [1] Akça Z. The construction of the cartesian group plane of order 25. MSc, University of Anadolu, Eskişehir, Turkey, 1991.
  • [2] Akça Z, Günaltılı İ. On the (k,3)-arcs of CPG(2,25,5). Anadolu University Journal of Science and–B Theoretical Sciences, 2012; 2 - 1 : 21-27.
  • [3] Bayar A, Akça Z, Ekmekçi S. On Embedding the Projective Plane PG(2,4) to the Projective Space P(4,4). New Trends in Mathematical Sciences, 2022: 10- 4: 142–150.
  • [4] Ekmekçi S, Bayar A, Akça Z. On The Projective Planes in Projective Space PG(4,4). Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 2022: 38- 3: 519–524.
  • [5] Ekmekçi S, Bayar A, Altintaş Kahriman E, Akça Z. On the Complete (k,2)- arcs of the Hall plane of order 9. International Journal of Advanced Research in Computer Science and Software Engineering, 2016; 6-10: 282–288.
  • [6] Panella, G. Una Classe Di Sistemi Cartesiani. Atti Della Accademia Nazionale Lincei Rendiconti, 1965; 38; 480-485.

SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE

Year 2023, Volume: 11 Issue: 2, 143 - 147, 28.08.2023

Ziya Akça

https://doi.org/10.20290/estubtdb.1302633

Abstract

Let π be the projective plane of order 25 coordinatised by elements of the smallest cartesian group. In this work, in some cases depending on the choice of the regular quadrangle it is shown that there is no any projective subplane of order 3 of π.

Keywords

Cartesian group Algebraic structure Projective plane

References

  • [1] Akça Z. The construction of the cartesian group plane of order 25. MSc, University of Anadolu, Eskişehir, Turkey, 1991.
  • [2] Akça Z, Günaltılı İ. On the (k,3)-arcs of CPG(2,25,5). Anadolu University Journal of Science and–B Theoretical Sciences, 2012; 2 - 1 : 21-27.
  • [3] Bayar A, Akça Z, Ekmekçi S. On Embedding the Projective Plane PG(2,4) to the Projective Space P(4,4). New Trends in Mathematical Sciences, 2022: 10- 4: 142–150.
  • [4] Ekmekçi S, Bayar A, Akça Z. On The Projective Planes in Projective Space PG(4,4). Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 2022: 38- 3: 519–524.
  • [5] Ekmekçi S, Bayar A, Altintaş Kahriman E, Akça Z. On the Complete (k,2)- arcs of the Hall plane of order 9. International Journal of Advanced Research in Computer Science and Software Engineering, 2016; 6-10: 282–288.
  • [6] Panella, G. Una Classe Di Sistemi Cartesiani. Atti Della Accademia Nazionale Lincei Rendiconti, 1965; 38; 480-485.
There are 6 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Ziya Akça 0000-0001-6379-0546

Publication Date August 28, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Akça, Z. (2023). SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 11(2), 143-147. https://doi.org/10.20290/estubtdb.1302633
AMA Akça Z. SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. August 2023;11(2):143-147. doi:10.20290/estubtdb.1302633
Chicago Akça, Ziya. “SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 11, no. 2 (August 2023): 143-47. https://doi.org/10.20290/estubtdb.1302633.
EndNote Akça Z (August 1, 2023) SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 11 2 143–147.
IEEE Z. Akça, “SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 11, no. 2, pp. 143–147, 2023, doi: 10.20290/estubtdb.1302633.
ISNAD Akça, Ziya. “SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 11/2 (August 2023), 143-147. https://doi.org/10.20290/estubtdb.1302633.
JAMA Akça Z. SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2023;11:143–147.
MLA Akça, Ziya. “SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 11, no. 2, 2023, pp. 143-7, doi:10.20290/estubtdb.1302633.
Vancouver Akça Z. SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2023;11(2):143-7.