Representing and Counting the Subgroups of the Group Zm×Zn-Reference-Cited by-同舟云学术

Representing and Counting the Subgroups of the Group Zm×Zn

Published:2014-10-16 Issue: Volume:2014 Page:1-6
ISSN:2356-7511
Container-title:Journal of Numbers
language:en
Short-container-title:Journal of Numbers

Author:

Hampejs Mario¹,Holighaus Nicki²,Tóth László³⁴^ORCID,Wiesmeyr Christoph¹

Affiliation:

1. NuHAG, Faculty of Mathematics, University of Vienna, Oskar Morgenstern Platz 1, 1090 Vienna, Austria

2. Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, 1040 Vienna, Austria

3. Department of Mathematics, University of Pécs, Ifjúság Útja 6, Pécs 7624, Hungary

4. Institute of Mathematics, University of Natural Resources and Life Sciences, Gregor-Mendel-Straße 33, 1180 Vienna, Austria

Abstract

We deduce a simple representation and the invariant factor decompositions of the subgroups of the group Zm×Zn, where m and n are arbitrary positive integers. We obtain formulas for the total number of subgroups and the number of subgroups of a given order.

Funder

Austrian Science Fund

Publisher

Hindawi Limited

Link

http://downloads.hindawi.com/archive/2014/491428.pdf

Reference20 articles.

1. A Group Theoretic Approach to a Famous Partition Formula

2. Gaussian binomials and the number of sublattices

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