Table of Contents
Journal of Numbers
Volume 2014, Article ID 491428, 6 pages
http://dx.doi.org/10.1155/2014/491428
Research Article

Representing and Counting the Subgroups of the Group

1NuHAG, Faculty of Mathematics, University of Vienna, Oskar Morgenstern Platz 1, 1090 Vienna, Austria
2Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, 1040 Vienna, Austria
3Department of Mathematics, University of Pécs, Ifjúság Útja 6, Pécs 7624, Hungary
4Institute of Mathematics, University of Natural Resources and Life Sciences, Gregor-Mendel-Straße 33, 1180 Vienna, Austria

Received 28 July 2014; Accepted 14 September 2014; Published 16 October 2014

Academic Editor: Andrej Dujella

Copyright © 2014 Mario Hampejs et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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