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

Lijian An; Ruifang Hu; Qinhai Zhang

doi:10.1007/s11425-013-4735-5

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arXiv · 1310.5503

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

Lijian An·Ruifang Hu·Qinhai Zhang

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Abstract

In this paper, we completely classify the finite $p$-groups $G$ such that $\Phi(G')G_3\le C_p^2$, $\Phi(G')G_3\le Z(G)$ and $G/\Phi(G')G_3$ 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.

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Lijian An, Ruifang Hu, Qinhai Zhang. 2013-10-21. Finite $p$-groups with a minimal non-abelian subgroup of index $p$ (IV). https://doi.org/10.1007/s11425-013-4735-5

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