TY  - JOUR
T1  - SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE
TT  - SOME RESULTS ON THE SMALLEST CARTESIAN GROUP PLANE
AU  - Akça, Ziya
PY  - 2023
DA  - August
DO  - 10.20290/estubtdb.1302633
JF  - Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler
JO  - Estuscience - Theory
PB  - Eskişehir Teknik Üniversitesi
WT  - DergiPark
SN  - 2667-419X
SP  - 143
EP  - 147
VL  - 11
IS  - 2
LA  - en
AB  - 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.
KW  - Cartesian group
KW  - Algebraic structure
KW  - Projective plane
N2  - 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.
CR  - [1]	Akça Z. The construction of the cartesian group plane of order 25. MSc, University of Anadolu, Eskişehir, Turkey, 1991.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [6]	Panella, G. Una Classe Di Sistemi Cartesiani. Atti Della Accademia Nazionale Lincei Rendiconti, 1965; 38; 480-485.
UR  - https://doi.org/10.20290/estubtdb.1302633
L1  - https://dergipark.org.tr/tr/download/article-file/3165670
ER  -