arXiv subjects

Qinhai Zhang

Publications and source records attributed to Qinhai Zhang.

3 recordsLinked to original sources

arXiv2014

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

Suppose that $G$ is a finite $p$-group. If all subgroups of index $p^t$ of $G$ are abelian and at least one subgroup of index $p^{t-1}$ of $G$ is not abelian, then $G$ is called an $\mathcal{A}_t$-group. In this paper, some information about $\mathcal{A}_t$-groups are obtained and $\mathcal{A}_3$-groups are completely classified. This solves an {\it old problem} proposed by Berkovich and Janko in their book. Abundant information about $\mathcal{A}_3$-groups are given.

math.GR↗

arXiv2014

On Finite Metahamiltonian p-Groups

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generalization of Hamiltonian groups. In this paper, the properties of finite metahamiltonian $p$-groups are investigated.

math.GR↗

arXiv2014

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

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

math.GR↗