Subgroups and Orbits by Companion Matrix in Three Dimensional Projective Space

Main Article Content

Emad Bakr Al-Zangana
https://orcid.org/0000-0001-6415-1930
Nada Yassen Kasm Yahya
https://orcid.org/0000-0002-1354-4758

Abstract

The aim of this paper is to construct cyclic subgroups of the projective general linear group over  from the companion matrix, and then form caps of various degrees in . Geometric properties of these caps as secant distributions and index distributions are given and determined if they are complete. Also, partitioned of  into disjoint lines is discussed.

Article Details

How to Cite
1.
Subgroups and Orbits by Companion Matrix in Three Dimensional Projective Space. Baghdad Sci.J [Internet]. 2022 Aug. 1 [cited 2024 Apr. 25];19(4):0805. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6229
Section
article

How to Cite

1.
Subgroups and Orbits by Companion Matrix in Three Dimensional Projective Space. Baghdad Sci.J [Internet]. 2022 Aug. 1 [cited 2024 Apr. 25];19(4):0805. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6229

References

‎ Kiss G and Szonyi T. Finite geometries. 1st Edition. Chapman and Hall/CRC. 2020.‎

Hirschfeld JWP. Finite Projective spaces of three dimensions. Oxford University Press, ‎Oxford.1985.‎

Davydov AA, Marcugini S and Pambianco F. Complete caps in projective spaces PG(n,q). J. Geom. 2008; 80:23-‎‎30.‎

Kasm Yahya NY. Applications geometry of space in PG(3,P). Journal of Interdisciplinary Mathematics. 2021. To ‎appear.‎

Kareem FF. The Construction of Complete (k;n)-arcs in 3-dimensional projective Space Over Galois Field ‎GF(4). Mustansiriyah Journal for Sciences and Education. 2013; 1:183-196.‎

Davydov A. On the spectrum of sizes of complete caps in projective spaces PG(n,q) of small dimension. ‎Eleventh International Workshop on Algebraic and Combinatorial Coding Theory June 16-22, 2008, Pamporovo, ‎Bulgaria. 2008:57-62.‎

Bartoli D and Davydov AA. New upper bounds on the smallest size of a complete cap in the space PG(3,q). ‎Seventh International Workshop on Optimal Codes and Related Topics September 6-12, 2013, Albena, Bulgaria pp. ‎‎2013:26-32.‎

Thas J. On k-caps in PG(n,q), with q even and n≥3. Discrete Mathematics. 2018;341(5):1459-1471.‎

Abdulla AA and Kasm Yahya NY. Application of algebraic geometry in three dimensional projective space ‎PG (3,7). Journal of Physics: Conference Series. 2020; 1591.‎

Anbar N, Bartoli D, Giulietti M and Platoni I. Small complete caps from singular cubics, II. J. Algebr. ‎Comb.2015; 41:85–216.‎

Al-Zangana EB. Splitting of PG(1,27) by sets and orbits, and arcs on the conic. Iraqi Journal of Science. ‎‎2021; ‎‎62(6): To appear. ‎

Al-Seraji N.A.M and Al-Ogali RAB. The group action on a projective plane over finite field of order sixteen. Iraqi ‎Journal of Science. 2017;58(3).‎

Al-Zangana EB and Joudah SA. Action of groups on the projective plane over the field (

Similar Articles

You may also start an advanced similarity search for this article.