The Lattice Structure of The Subgroups of
Order 27 In The Subgroup Lattices of 3X3
Matrices Over Z3

V. Durai murugan; R. Seethalakshmi; Dr.P.Namasivayam

doi:https://doi.org/10.14445/22315373/IJMTT-V66I9P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P505

The Lattice Structure of The Subgroups of Order 27 In The Subgroup Lattices of 3X3 Matrices Over Z3

V. Durai murugan, R. Seethalakshmi, Dr.P.Namasivayam

Citation :

V. Durai murugan, R. Seethalakshmi, Dr.P.Namasivayam, "The Lattice Structure of The Subgroups of Order 27 In The Subgroup Lattices of 3X3 Matrices Over Z3," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 26-36, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P505

Abstract

Let G be the set of all 3 X 3 non-singular matrices (a b c d e f g h i), where a,b,c,d,e,f,g,h,i are integers modulo p. Then G is a group under matrix multiplication modulo p, of order ( pn-1)(pn-p2).. ...(pn-pn-1). Let G be the subgroup of G defined by G = { (a b c d e f g h i) ε G : | a b c d e f g h i| = 1}. Then G is of order (pn-1)(pn-p)(pn-p2)....(pn-pn-1)/p-1. Let L(G) be the lattice formed by all subgroups G. In this paper, we give the structure of the subgroups of order 27 of L(G) in the case when P=3.

Keywords

Matrix group, subgroups, Lagrange’s theorem, Lattice, Atom.

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