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The Scientific World Journal
Volume 2013 (2013), Article ID 430870, 3 pages
http://dx.doi.org/10.1155/2013/430870
Research Article

On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups

1School of Mathematics and Information Science, Yantai University, Yantai 264005, China
2Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Lyngby, Denmark

Received 3 August 2013; Accepted 11 September 2013

Academic Editors: J. Hoff da Silva and J. Park

Copyright © 2013 Jiangtao Shi and Cui Zhang. 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

Let be a finite group and the set of the numbers of conjugates of noncyclic proper subgroups of . We prove that (1) if , then is solvable, and (2) is a nonsolvable group with if and only if or or or .