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Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1229-1233
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Let $G$ be a finite group. We prove that if every self-centralizing subgroup of $G$ is nilpotent or subnormal or a TI-subgroup, then every subgroup of $G$ is nilpotent or subnormal. Moreover, $G$ has either a normal Sylow $p$-subgroup or a normal $p$-complement for each prime divisor $p$ of $|G|$.
Let $G$ be a finite group. We prove that if every self-centralizing subgroup of $G$ is nilpotent or subnormal or a TI-subgroup, then every subgroup of $G$ is nilpotent or subnormal. Moreover, $G$ has either a normal Sylow $p$-subgroup or a normal $p$-complement for each prime divisor $p$ of $|G|$.
DOI : 10.21136/CMJ.2021.0512-20
Classification : 20D10
Keywords: self-centralizing; nilpotent; TI-subgroup; subnormal; $p$-complement 
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     title = {Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a {TI-subgroup}},
     journal = {Czechoslovak Mathematical Journal},
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Shi, Jiangtao; Li, Na. Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1229-1233. doi: 10.21136/CMJ.2021.0512-20

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