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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Some new characterizations of $p$-supersoluble and $p$-nilpotent groups are obtained.
📌 3 Key Takeaways
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Objective & Hypothesis:A subgroup $H$ of a group $G$ is said to be $\tau$-quasinormal in $G$ if $H$ permutes with every Sylow subgroup $Q$ of $G$ such that $(|H|,|Q|)=1$ and $(|H|,|Q|^G)\neq1$; $H$ is called partially $\tau$-quasinormal in $G$ if $G$ has a normal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $H\cap T\leq H_{\tau G}$, where $H_{\tau G}$ is the subgroup generated by all those subgroups of $H$ which are $\tau$-quasinormal in $G$.
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Key Findings & Data:In this paper, we investigate the influence of some partially $\tau$-quasinormal subgroups on the structureof finite group.
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Conclusion & Impact:Some new characterizations of $p$-supersoluble and $p$-nilpotent groups are obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$S$-quasinormal · partially $\tau$-quasinormal · $p$-supersoluble
Abstract
A subgroup $H$ of a group $G$ is said to be $\tau$-quasinormal in $G$ if $H$ permutes with every Sylow subgroup $Q$ of $G$ such that $(|H|,|Q|)=1$ and $(|H|,|Q|^G)\neq1$; $H$ is called partially $\tau$-quasinormal in $G$ if $G$ has a normal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $H\cap T\leq H_{\tau G}$, where $H_{\tau G}$ is the subgroup generated by all those subgroups of $H$ which are $\tau$-quasinormal in $G$. In this paper, we investigate the influence of some partially $\tau$-quasinormal subgroups on the structureof finite group. Some new characterizations of $p$-supersoluble and $p$-nilpotent groups are obtained.
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Cite This Article
Li, C., QİAO, S., HUANG, J. (2017). The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 3, 389–395. https://ajindex.com/articles/669473