Geodesic
Finite groups with bicyclic Sylow subgroups in Fitting factors
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 304-307 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Estimates of the derived length, nilpotent length, and $p$-length are obtained for a finite solvable group $G$ in which Sylow subgroups in factors of the chain $\Phi(G)=G_0\subset G_1\subset\ldots\subset G_{m-1}\subset G_m=F(G)$ of subgroups normal in $G$ are bicyclic, i.e., are factorized by two cyclic subgroups. Here, $\Phi(G)$ is the Frattini subgroup of $G$ and $F(G)$ is the Fitting subgroup of $G$. In particular, the derived length of $G/\Phi(G)$ is at most 5, the nilpotent length of $G$ is at most 4, and the $p$-length of $G$ is at most 2 for every prime $p$.
Mots-clés : finite solvable group
Keywords: Frattini subgroup, Fitting subgroup, derived length, nilpotent length, $p$-length, $A_4$-free group. 
@article{TIMM_2013_19_3_a31,
     author = {A. A. Trofimuk},
     title = {Finite groups with bicyclic {Sylow} subgroups in {Fitting} factors},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {304--307},
     year = {2013},
     volume = {19},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a31/}
}
TY  - JOUR
AU  - A. A. Trofimuk
TI  - Finite groups with bicyclic Sylow subgroups in Fitting factors
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2013
SP  - 304
EP  - 307
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a31/
LA  - ru
ID  - TIMM_2013_19_3_a31
ER  - 
%0 Journal Article
%A A. A. Trofimuk
%T Finite groups with bicyclic Sylow subgroups in Fitting factors
%J Trudy Instituta matematiki i mehaniki
%D 2013
%P 304-307
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a31/
%G ru
%F TIMM_2013_19_3_a31
A. A. Trofimuk. Finite groups with bicyclic Sylow subgroups in Fitting factors. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 304-307. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a31/

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

[2] Monakhov V. S., Trofimuk A. A., “On a finite group having a normal series whose factors have bicyclic Sylow subgroups”, Commun. in Algebra, 39:9 (2011), 3178–3186 | DOI | MR | Zbl

[3] Baer R., “Supersolvable immersion”, Can. J. Math., 11 (1959), 353–369 | DOI | MR | Zbl

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

[5] Shemetkov L. A., Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp. | MR | Zbl

[6] Monakhov V. S., Trofimuk A. A., “O konechnykh razreshimykh gruppakh fiksirovannogo ranga”, Sib. mat. zhurn., 52:5 (2011), 1123–1137 | MR | Zbl