On the Embedding of an Arc into Cubic Curves in a Finite Projective Plane of Order Seven

Najm A. M. Al-Seraji; Raad Ibrahim kute

doi:10.23851/mjs.v30i1.527

On the Embedding of an Arc into Cubic Curves in a Finite Projective Plane of Order Seven

Authors

Najm A. M. Al-Seraji Department of Mathematics, College of Science, Mustansiriyah University
Raad Ibrahim kute Department of Mathematics, College of Science, Mustansiriyah University

DOI:

https://doi.org/10.23851/mjs.v30i1.527

Abstract

The main aims of this research are to find the stabilizer groups of cubic curves over a finite field of order 7 and studying the properties of their groups and then constructing the arcs of degree 2 which are embedding in cubic curves of even size which are considering as the arcs of degree 3. Also drawing all these arcs.

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Author Biography

Raad Ibrahim kute, Department of Mathematics, College of Science, Mustansiriyah University

mathematics department

References

J. W. P. Hirschfeld, "Projective geometries over finite fields", 2nd Edition, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1980.

N. A. M. Al-Seraji, "The Geometry of The Plane of order Seventeen and its Application to Error-correcting codes", Ph.D. Thesis, University of Sussex , UK, 2010.

E. M. Al-Zangana, "The Geometry of The Plane of order nineteen and its application to error-correcting codes", Ph. D. Thesis, University of Sussex, United Kingdom, 2011.

E. M. Al-Zangana, "On Non-Singular Plane Cubic Curves over F_q ,q=2,3,5,7" College of education J.No.1, 2013.

E. M. Al-Zangana,"Complete and Incomplete Elliptic curves over the finite field of order 11 and 13", Al-Mustansiriyah Journal of Science, Vol.24 ,No 1, 2013.

A. D. Thomas and G. V. Wood,"Group tables", Shiva Mathematics Series, Series 2, Devon print Group , Exeter , Devon , UK, 1980.

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Key Dates

Published

15-08-2019

Issue

Vol. 30 No. 1 (2019)

Section

Original Article

License

(Starting May 5, 2024) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.

How to Cite

[1]

N. A. M. Al-Seraji and R. I. kute, “On the Embedding of an Arc into Cubic Curves in a Finite Projective Plane of Order Seven”, Al-Mustansiriyah J. Sci., vol. 30, no. 1, pp. 158–168, Aug. 2019, doi: 10.23851/mjs.v30i1.527.