Table of Contents
Algebra
Volume 2013, Article ID 135045, 3 pages
http://dx.doi.org/10.1155/2013/135045
Research Article

A Note on Hobby’s Theorem of Finite Groups

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 10 March 2013; Accepted 27 May 2013

Academic Editor: Ricardo L. Soto

Copyright © 2013 Qingjun Kong. 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

It is well known that the Frattini subgroups of any finite groups are nilpotent. If a finite group is not nilpotent, it is not the Frattini subgroup of a finite group. In this paper, we mainly discuss what kind of finite nilpotent groups cannot be the Frattini subgroup of some finite groups and give some results. Moreover, we generalize Hobby’s Theorem.