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Keywords:
self-centralizing; nilpotent; TI-subgroup; subnormal; $p$-complement
self-centralizing; nilpotent; TI-subgroup; subnormal; $p$-complement
Summary:
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 $|G|$.
References:
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