Geodesic
Products of $\pi$-nilpotent subgroups
Sbornik. Mathematics, Tome 187 (1996) no. 9, pp. 1349-1354 
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/
@article{SM_1996_187_9_a4,
     author = {V. N. Tyutyanov},
     title = {Products of $\pi$-nilpotent subgroups},
     journal = {Sbornik. Mathematics},
     pages = {1349--1354},
     year = {1996},
     volume = {187},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_9_a4/}
}
TY  - JOUR
AU  - V. N. Tyutyanov
TI  - Products of $\pi$-nilpotent subgroups
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 1349
EP  - 1354
VL  - 187
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_9_a4/
LA  - en
ID  - SM_1996_187_9_a4
ER  - 
%0 Journal Article
%A V. N. Tyutyanov
%T Products of $\pi$-nilpotent subgroups
%J Sbornik. Mathematics
%D 1996
%P 1349-1354
%V 187
%N 9
%U http://geodesic.mathdoc.fr/item/SM_1996_187_9_a4/
%G en
%F SM_1996_187_9_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Gorenstein D., Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985 | MR | Zbl

[2] Huppert B., Endliche Gruppen, V. I, Springer-Verlag, Berlin–New York, 1967 | MR | Zbl

[3] Chunikhin S. A., Podgruppy konechnykh grupp, Nauka i tekhnika, Minsk, 1964 | MR | Zbl

[4] Alperin J. L., Brauer R., Gorenstein D., “Finite groups with quasidihedral and wreathed Sylow $2$-subgroups”, Trans. Amer. Math. Soc., 151:1 (1970), 1–261 | DOI | MR | Zbl

[5] Alperin J. L., Brauer R., Gorenstein D., “Finite simple groups of $2$-rank two”, Scripta Comput. Sci. Appl. Math., 29:3–4 (1973), 191–214 | MR | Zbl

[6] Alperin J. L., Brauer R., Gorenstein D., The extanded $ZJ$-theorem, Proc. Gaintsville Conf., Amsterdam, 1972, 6–7

[7] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A., An Atlas of finite groups, Claredon Press, Oxford, 1985 | MR | Zbl

[8] Kazarin L. S., “O probleme Sepa”, Izv. AN SSSR, 50:3 (1986), 467–495 | MR