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

László Tóth

doi:10.2478/tmmp-2014-0021

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

Tatra Mountains Mathematical Publications

Volume 59 (2014): Issue 1 (June 2014)

By: László Tóth

Open Access

|Mar 2015

Abstract

Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m× Z_n 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.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2014-0021 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 93 - 103

Submitted on: Sep 29, 2014

Published on: Mar 11, 2015

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

finite abelian group of rank two

Related subjects:

Mathematics,

General mathematics

© 2015 László Tóth, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 59 (2014): Issue 1 (June 2014)