Geodesic
On the derived $\pi$-length of a finite $\pi$-solvable group with a given $\pi$-Hall subgroup
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 215-223 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $G_\pi$ be a $\pi$-Hall subgroup of a finite $\pi$-solvable group $G$, and let $M$ be a maximal subgroup of $G_\pi$. We find estimates for the derived $\pi$-length $l^a_\pi(G)$ of $G$ depending on the structure of the subgroups $G_\pi$ or $M$. We consider the situation where all proper subgroups in these subgroups are abelian or nilpotent. In particular, we prove that $l_\pi^a(G)\le5$ if $M$ is a minimal nonnilpotent group.
Mots-clés : finite $\pi$-solvable group
Keywords: Hall subgroup, derived length. 
@article{TIMM_2013_19_3_a21,
     author = {V. S. Monakhov and D. V. Gritsuk},
     title = {On the derived $\pi$-length of a~finite $\pi$-solvable group with a~given $\pi${-Hall} subgroup},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {215--223},
     year = {2013},
     volume = {19},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a21/}
}
TY  - JOUR
AU  - V. S. Monakhov
AU  - D. V. Gritsuk
TI  - On the derived $\pi$-length of a finite $\pi$-solvable group with a given $\pi$-Hall subgroup
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2013
SP  - 215
EP  - 223
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a21/
LA  - ru
ID  - TIMM_2013_19_3_a21
ER  - 
%0 Journal Article
%A V. S. Monakhov
%A D. V. Gritsuk
%T On the derived $\pi$-length of a finite $\pi$-solvable group with a given $\pi$-Hall subgroup
%J Trudy Instituta matematiki i mehaniki
%D 2013
%P 215-223
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a21/
%G ru
%F TIMM_2013_19_3_a21
V. S. Monakhov; D. V. Gritsuk. On the derived $\pi$-length of a finite $\pi$-solvable group with a given $\pi$-Hall subgroup. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 215-223. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a21/

[1] Huppert B., Endliche Gruppen, v. I, Springer-Verlag, Berlin, 1967, 793 pp. | MR | Zbl

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

[3] Monakhov V. S., Shpyrko O. A., “O nilpotentnoi $\pi$-dline konechnoi $\pi$-razreshimoi gruppy”, Diskret. matematika, 13:3 (2001), 145–152 | DOI | MR | Zbl

[4] Monakhov V. S., Shpyrko O. A., “O nilpotentnoi $\pi$-dline maksimalnykh podgrupp konechnykh $\pi$-razreshimykh grupp”, Vestn. Mosk. un-ta. Ser. 1: Matematika, mekhanika, 2009, no. 6, 3–8 | MR

[5] Gritsuk D. V., Monakhov V. S., Shpyrko O. A., “O konechnykh $\pi$-razreshimykh gruppakh s bitsiklicheskimi silovskimi podgruppami”, Problemy matematiki, fiziki i tekhniki, 14:1 (2013), 61–66

[6] Shmidt O. Yu., “Gruppy, vse podgruppy kotorykh spetsialnye”, Mat. sb., 31:3–4 (1924), 366–372 | Zbl

[7] Golfand Yu. A., “O gruppakh, vse podgruppy kotorykh spetsialnye”, Dokl. AN SSSR, 60:8, 1948

[8] Berkovich Y., Groups of prime power order, v. 1, Walter de Gruyter, Berlin, 2008, 512 pp. | MR | Zbl

[9] Monakhov V. S., “Proizvedenie konechnykh grupp, blizkikh k nilpotentnym”, Konechnye gruppy, Cb. st., Nauka i tekhnika, Minsk, 1975, 70–100

[10] Zhurtov A. Kh., Syskin S. A., “O gruppakh Shmidta”, Sib. mat. zhurn., 28:2 (1987), 74–78 | MR | Zbl

[11] Chernikov N. S., “Groups with an abelian maximal subgroup”, Tr. In-ta matematiki NAN Belarusi, 16, no. 1, 2008, 86–92

[12] Belonogov V. A., “Konechnye razreshimye gruppy s nilpotentnymi 2-maksimalnymi podgruppami”, Mat. zametki, 3:1 (1968), 21–32 | MR | Zbl

[13] Sistema kompyuternoi algebry GAP 4.4.12, elektron. resurs, URL: , 2009 http://www.gap-system.org/ukrgap/gapbook/manual.pdf