Intersection of maximal subgroups which are not minimal nonabelian of finite p-groups

ABSTRACT

Let G be a finite p-group and ${\Phi }_{N{\mathcal{𝒜}}_{1}M}\left(G\right)$ denote the intersection of maximal subgroups of G which are not minimal nonabelian. We investigate the influence of ${\Phi }_{N{\mathcal{𝒜}}_{1}M}\left(G\right)$ on the structure of finite p-groups. In particular, a question proposed by Berkovich and Janko is solved.

KEYWORDS:

• Finite p-groups
• maximal subgroups
• minimal nonabelian subgroups

AMS SUBJECT CLASSIFICATIONS:

• 20D15
• 20D25