| Finite Groups Whose Norm Quotient Groups Have Cyclic Sylow Subgroups |
| Received:February 05, 2021 Revised:October 16, 2021 |
| Key Words:
norm Dedekind group Hamiltonian group $\pi$-group structure of finite group Sylow subgroup
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11661023) and the Service Industry Development Guide of Guizhou Province (Grant No.QianFaGaiFuWu[2018]1181). |
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| Abstract: |
| Let $G$ be a finite group and $N(G)$ be its norm. Then $N(G)$ is a characteristic subgroup of $G$ which normalizes every subgroup of $G$. In this paper, we will study the structure of $G$ under one of the following conditions: 1) norm quotient group $G/N(G)$ is cyclic; 2) all Sylow subgroups of $G/N(G)$ are cyclic and in particular if the order of $G/N(G)$ is a square-free number. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.02.006 |
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