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

Abstract

In this paper, we completely classify the finite $p$-groups $G$ such that $\Phi (G^{\prime })G_3\le C_p^2$, $\Phi (G^{\prime })G_3\le Z(G)$ and $G/\Phi (G^{\prime })G_3$ is minimal non-abelian. This paper is a part of the classification of finite $p$-groups with a minimal non-abelian subgroup of index $p$. Together with other four papers, we solve a problem proposed by Y. Berkovich.

References in corpus (1)

• Finite $p$-groups all of whose subgroups of index $p^3$ are abelian

Cited by in corpus (1)

• Finite $p$-groups all of whose subgroups of index $p^3$ are abelian