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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 3 | Year 2020 | Article Id. IJMTT-V66I3P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I3P506

A Study on Pseudo 0 - Distributivity And Super 0 – Distributivity In The Subgroup Lattice of 2X2 Matrices Over Z3, Z5 AND Z7


Dr. R. Murugesan, R. Seethalakshmi, Dr.P.Namasivayam
Citation :

Dr. R. Murugesan, R. Seethalakshmi, Dr.P.Namasivayam, "A Study on Pseudo 0 - Distributivity And Super 0 – Distributivity In The Subgroup Lattice of 2X2 Matrices Over Z3, Z5 AND Z7," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 3, pp. 33-38, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I3P506

Abstract

In this paper we verify the lattice theoretic properties like the pseudo 0 - distributivity and super 0 – distributivity in the subgroup lattice of 2x2 matrices over z3, z5 and z7.

Keywords
Matrix group, subgroups, Lattice, pseudo 0 – distributivity, super 0 -distributivity
References

[1] Bourbaki N. Elements of Mathematics, Algebra I, Chapter 1-3 Springer Verlag Berlin Heidelberg, New York, London Paris Tokio.1974.
[2] Fraleigh. J.B, A first course in Abstract Algebra, Addison – Wesley,London, 1992.
[3] Gardiner. C.F, A first course in group theory, Springer-Verlag, Berlin,1997.
[4] Gratzer. G, General Lattice theory:BirkhauserVeslag, Basel,1998.
[5] Herstien I.N, Topics in Algebra, John Wiley and sons, New York,1975.
[6] JebarajThiraviam. D, A Study on some special types of lattices, Ph.D thesis, ManonmaniamSundaranar University,2015.
[7] Vethamanickam. A., and JebarajThiraviam., On Lattices of Subgroups, Int.Journal of Mathematical Archiv-6(9), 2015,1-11.

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