Geodesic
Dependence of the derived $p$-length of a $p$-solvable group on the order of its Sylow $p$-subgroup
Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 58-60.

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

It is proved that the derived $p$-length $l_p^a(G)$ of the $p$-solvable group $G$ in which the Sylow $p$-subgroup has order $p^n$ is at most $1+\frac n2$ and if $p\not\in\{2,3\}$ then $l_p^a(G)\leqslant\frac{n+1}2$.
Keywords: finite group, Sylow subgroup, derived $p$-length.
Mots-clés : $p$-solvable group 
@article{PFMT_2014_3_a10,
     author = {D. V. Gritsuk},
     title = {Dependence of the derived $p$-length of a $p$-solvable group on the order of its {Sylow} $p$-subgroup},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {58--60},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_3_a10/}
}
TY  - JOUR
AU  - D. V. Gritsuk
TI  - Dependence of the derived $p$-length of a $p$-solvable group on the order of its Sylow $p$-subgroup
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2014
SP  - 58
EP  - 60
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2014_3_a10/
LA  - ru
ID  - PFMT_2014_3_a10
ER  - 
%0 Journal Article
%A D. V. Gritsuk
%T Dependence of the derived $p$-length of a $p$-solvable group on the order of its Sylow $p$-subgroup
%J Problemy fiziki, matematiki i tehniki
%D 2014
%P 58-60
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2014_3_a10/
%G ru
%F PFMT_2014_3_a10
D. V. Gritsuk. Dependence of the derived $p$-length of a $p$-solvable group on the order of its Sylow $p$-subgroup. Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 58-60. http://geodesic.mathdoc.fr/item/PFMT_2014_3_a10/

[1] V. S. Monakhov, Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006, 207 pp.

[2] B. Huppert, Endliche Gruppen, v. I, Springer, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[3] P. Hall, G. Higman, “The $p$-lengh of a $p$-soluble groups and reduction theorems for Burnside's problem”, Proc. London Math. Soc., 3:7 (1956), 1–42 | DOI | MR | Zbl

[4] E. G. Bryukhanova, “Svyaz mezhdu 2-dlinoi i proizvodnoi dlinoi silovskoi 2-podgruppy konechnoi razreshimoi gruppy”, Matematicheskie zametki, 29:2 (1981), 161–170 | MR

[5] A. Mann, “The derived length of $p$-groups”, J. Algebra, 224 (2000), 263–267 | DOI | MR | Zbl

[6] V. S. Monakhov, “Konechnye gruppy s polunormalnoi khollovoi podgruppoi”, Matematicheskie zametki, 80:4 (2006), 573–581 | DOI | MR | Zbl

[7] D. V. Gritsuk, V. S. Monakhov, O. A. Shpyrko, “O proizvodnoi $\pi$-dline $\pi$-razreshimoi gruppy”, Vestnik BGU. Seriya 1, 2012, no. 3, 90–95

[8] D. V. Gritsuk, V. S. Monakhov, O. A. Shpyrko, “O konechnykh $\pi$-razreshimykh gruppakh s bitsiklicheskimi silovskimi podgruppami”, Problemy fiziki, matematiki i tekhniki, 2013, no. 1(14), 61–66

[9] D. V. Gritsuk, “Proizvodnaya $\pi$-dlina $\pi$-razreshimoi gruppy, silovskie $p$-podgruppy kotoroi libo bitsiklicheskie, libo imeyut poryadok $p^3$”, Problemy fiziki, matematiki i tekhniki, 2014, no. 2(19), 54–58

[10] V. S. Monakhov, O. A. Shpyrko, “O nilpotentnoi $\pi$-dline maksimalnykh podgrupp konechnykh $\pi$-razreshimykh grupp”, Vectnik Mosk. un-ta. Seriya 1. Matematika. Mekhanika, 2009, no. 6, 3–8