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

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

Group Theory 2023-07-19 v2

Authors: 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.

Keywords

finite p-groups minimal non-abelian subgroup group classification index p Berkovich problem

Cite

@article{arxiv.1310.5503,
  title  = {Finite $p$-groups with a minimal non-abelian subgroup of index $p$ (IV)},
  author = {Lijian An and Ruifang Hu and Qinhai Zhang},
  journal= {arXiv preprint arXiv:1310.5503},
  year   = {2023}
}

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

Abstract

Keywords

Cite

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