Decomposition of Goursat Matrices and Subgroups of Zm x Zn

  • Brice Réné Amougou Mbarga University of Yaoundé I, Laboratory of Algebra, Geometry and Application, P.O.Box: 812, Yaoundé, Cameroon
Keywords: 2-factor, Goursat Lemma, group, matrix

Abstract

Given the number of subgroups of Zm x Zn, we deduce the Goursat matrix. The purpose of this paper is two-fold. A first and more concrete aim is to demonstrate that the triangular decomposition of the Goursat matrix may also be written out explicitly, and furthermore that the same is true of the inverse of these triangular factors.  A second and more abstract aim provides a containment relation property between subgroups of a direct product . Namely, if U2 ≤ U1 ≤ Zm x Zn, we provide necessary and sufficient conditions for U2 ≤ U1.

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Published
2021-05-21
How to Cite
Mbarga, B. R. A. (2021). Decomposition of Goursat Matrices and Subgroups of Zm x Zn. Earthline Journal of Mathematical Sciences, 6(2), 439-454. https://doi.org/10.34198/ejms.6221.439454
Section
Articles