Finite Groups Whose Norm Quotient Groups Have Cyclic Sylow Subgroups
Received:February 05, 2021  Revised:September 26, 2021
Key Word: norm, Dedekind group, Hamiltonian group, π-group, structure of finite group, Sylow subgroup  
Fund ProjectL:National Natural Science Foundation of China (11661023) and Guizhou Provincial Service Industry Development Guide fund project in 2018 (The Third Batch,No.QianFaGaiFuWu[2018]1181)
Author NameAffiliationAddress
Songliang Chen Guizhou Edcation University 贵州省贵阳市乌当区高新路115号贵州师范学院数学与大数据学院
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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.
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