Table of Contents
International Journal of Combinatorics
Volume 2014 (2014), Article ID 835125, 8 pages
http://dx.doi.org/10.1155/2014/835125
Research Article

Characterizing Finite Groups Using the Sum of the Orders of the Elements

1Department of Mathematics, Cedar Crest College, Allentown, PA 18104, USA
2Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, USA

Received 24 August 2014; Accepted 24 October 2014; Published 13 November 2014

Academic Editor: Laszlo A. Szekely

Copyright © 2014 Joshua Harrington 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 give characterizations of various infinite sets of finite groups under the assumption that and the subgroups of satisfy certain properties involving the sum of the orders of the elements of and . Additionally, we investigate the possible values for the sum of the orders of the elements of .