Geodesic
Products of $\pi$-nilpotent subgroups
Sbornik. Mathematics, Tome 187 (1996) no. 9, pp. 1349-1354

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Let $A$ and $B$ be $\pi$-nilpotent subgroups of a finite group $G$ and suppose that $(|G:A|,p)=(|G:B|,p)=1$ for all $p\in \pi$. It is proved that if $G$ is a product of $A$ and $B$ then $G$ is a $\pi$-nilpotent group. 
@article{SM_1996_187_9_a4,
     author = {V. N. Tyutyanov},
     title = {Products of $\pi$-nilpotent subgroups},
     journal = {Sbornik. Mathematics},
     pages = {1349--1354},
     publisher = {mathdoc},
     volume = {187},
     number = {9},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_9_a4/}
}
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V. N. Tyutyanov. Products of $\pi$-nilpotent subgroups. Sbornik. Mathematics, Tome 187 (1996) no. 9, pp. 1349-1354. http://geodesic.mathdoc.fr/item/SM_1996_187_9_a4/