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 A note on primitive subgroups of finite solvable groups Commun. Korean Math. Soc. 2013 Vol. 28, No. 1, 55-62 https://doi.org/10.4134/CKMS.2013.28.1.55Printed January 31, 2013 Xuanli He, Shouhong Qiao, and Yanming Wang Guangxi University, Guangdong University of Technology, Sun Yat-sen University Abstract : In \cite{J}, Johnson introduced the primitivity of subgroups and proved that a finite group $G$ is supersolvable if every primitive subgroup of $G$ has a prime power index in $G$. In that paper, he also posed an interesting problem: what a group looks like if all of its primitive subgroups are maximal. In this note, we give the detail structure of such groups in solvable case. Finally, we use the primitivity of some subgroups to characterize $T$-group and the solvable $PST_0$-groups. Keywords : finite groups, primitive subgroups, maximal subgroups, the solvable $PST_0$-groups MSC numbers : 20D10, 20D15 Downloads: Full-text PDF

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