A Note on Hobby's Theorem of Finite Groups. (12th June 2013)

• Record Type: Journal Article
• Authors: Kong, Qingjun
• Other Names: Soto Ricardo L. Academic Editor.
• Is Part Of: Algebra. Volume 2013(2013)
• Publication Date: 2013-06-12
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2013/135045
• Languages: English
• ISSNs: 2314-4106

Abstract

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.