<abstract xmlns="http://www.w3.org/1999/xhtml">Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Zm × Zn are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.</abstract>

Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Zm × Zn are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.

Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma

Institute of Mathematics Universität für Bodenkultur Gregor Mendel-Straße 33 A–1180 Vienna Austria

Department of Mathematics University of Pécs Ifjúság u. 6 H–7624 Pécs Hungary

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Subgroups of Finite Abelian Groups Having Rank Two via Goursat\u2019s Lemma"}

Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Zm × Zn are deduced, where m...

Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma

Published Online: Mar 11, 2015

Page range: 93 - 103

Received: Sep 29, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0021

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.