A Note on Hobby’s Theorem of Finite Groups

Abstract EN

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.