SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE

Yıl 2023, , 143 - 147, 28.08.2023

Ziya Akça

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

Öz

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.

Anahtar Kelimeler

Kartezyen grup, Projektif Düzlem, Cebirsel yapı

SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE

Öz

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.

Anahtar Kelimeler

Cartesian group, Algebraic structure, Projective plane

Kaynakça

• [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.