Geodesic
Finite group with given $c$-permutable subgroups
Algebra and discrete mathematics, no. 2 (2004), pp. 9-16

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Following [1] we say that subgroups $H$ and $T$ of a group $G$ are $c$-permutable in $G$ if there exists an element $x\in G$ such that $HT^x=T^xH$. We prove that a finite soluble group $G$ is supersoluble if and only if every maximal subgroup of every Sylow subgroup of $G$ is $c$-permutable with all Hall subgroups of $G$.
Keywords: finite group, maximal subgroup, Sylow subgroup, supersoluble group, $c$-permutable subgroup. 
@article{ADM_2004_2_a2,
     author = {Ahmad Alsheik Ahmad},
     title = {Finite group with given $c$-permutable subgroups},
     journal = {Algebra and discrete mathematics},
     pages = {9--16},
     publisher = {mathdoc},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2004_2_a2/}
}
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Ahmad Alsheik Ahmad. Finite group with given $c$-permutable subgroups. Algebra and discrete mathematics, no. 2 (2004), pp. 9-16. http://geodesic.mathdoc.fr/item/ADM_2004_2_a2/