Geodesic
Finite Groups in which Primary Subgroups have Cyclic Cofactors
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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In this paper, we prove the following theorem: Let $G$ be a group, $q$ be the largest prime divisor of $|G|$ and $\pi =\pi (G)\setminus \{q\}$. Suppose that the factor group $X/core_GX$ is cyclic for every $p$-subgroup $X$ of $G$ and every $p\in \pi$. Then: (1). $G$ is soluble and its Hall $\{2, 3\}'$-subgroup is normal in $G$ and is a dispersive group by Ore; (2). All Hall $\{2, 3\}$-subgroups of $G$ are metanilpotent; (3). Every Hall $p'$-subgroup of $G$ is a dispersive group by Ore, for every $p\in \{2, 3\}$; (4). $l_{r}(G)\leq1$, for all $r\in \pi (G)$.
Classification : 20D10, 20D20. 
@article{BMMS_2011_34_2_a12,
     author = {Yufeng Liu and Xiaolan Yi},
     title = {Finite {Groups} in which {Primary} {Subgroups} have {Cyclic} {Cofactors}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a12/}
}
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AU  - Xiaolan Yi
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Yufeng Liu; Xiaolan Yi. Finite Groups in which Primary Subgroups have Cyclic Cofactors. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a12/