Geodesic
The Formation of Finite Groups with a Supersolvable $\pi$-Hall Subgroup
Matematičeskie zametki, Tome 87 (2010) no. 2, pp. 280-286

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Let $G$ be a finite group having a $\pi$-subgroup $H$ such that $|G:H|$ is not divisible by the numbers in $\pi$. In this case, the subgroup $H$ is referred to as a $\pi$-Hall subgroup, and the group $G$ by itself is referred to as a $E_\pi$-group. If, moreover, the group $H$ is supersolvable, then $G$ is referred to as an $E_\pi^u$-group. It is proved in the paper that the class of all $E_\pi^u$-groups is a solvably saturated formation, and the proof is carried out without using the classification of finite groups.
Keywords: Hall subgroup, classification of finite groups, saturated formation, Frattini subgroup, monolithic group, subdirect product.
Mots-clés : supersolvable group, formation 
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     author = {Yi Xiaolan and L. A. Shemetkov},
     title = {The {Formation} of {Finite} {Groups} with a {Supersolvable} $\pi${-Hall} {Subgroup}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {280--286},
     publisher = {mathdoc},
     volume = {87},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_2_a9/}
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Yi Xiaolan; L. A. Shemetkov. The Formation of Finite Groups with a Supersolvable $\pi$-Hall Subgroup. Matematičeskie zametki, Tome 87 (2010) no. 2, pp. 280-286. http://geodesic.mathdoc.fr/item/MZM_2010_87_2_a9/