Finite $p$-groups with a minimal non-abelian subgroup of index $p$ (III)

Abstract

In this paper, we finished the classification of three-generator finite $p$-groups $G$ such that $\Phi(G)\le Z(G)$. This paper is a part of classification of finite $p$-groups with a minimal non-abelian subgroup of index $p$, and partly solved a problem proposed by Y. Berkovich.