Comptes Rendus
no. 11-12
Théorie des groupes
Influence of the number of Sylow subgroups on solvability of finite groups
Chimere Stanley Anabanti1 ; Alexander Moretó2  ; Mohammad Zarrin3
1 Institut für Analysis und Zahlentheorie, Technische Universität Graz (TU Graz), Graz 8010 Austria.
2 Departament de Matemàtiques, Universitat de València, 46100, Burjassot, València Spain.
3 Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran.
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1227-1230.

Let G be a finite group. We prove that if the number of Sylow 3-subgroups of G is at most 7 and the number of Sylow 5-subgroups of G is at most 1455, then G is solvable. This is a strong form of a recent conjecture of Robati.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.146
Classification : 20D10, 20D20, 20F16, 20F19
Chimere Stanley Anabanti 1 ; Alexander Moretó 2 ; Mohammad Zarrin 3

1 Institut für Analysis und Zahlentheorie, Technische Universität Graz (TU Graz), Graz 8010 Austria.
2 Departament de Matemàtiques, Universitat de València, 46100, Burjassot, València Spain.
3 Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2020__358_11-12_1227_0,
     author = {Chimere Stanley Anabanti and Alexander Moret\'o and Mohammad Zarrin},
     title = {Influence of the number of {Sylow} subgroups on solvability of finite groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1227--1230},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.146},
     language = {en},
}
TY  - JOUR
AU  - Chimere Stanley Anabanti
AU  - Alexander Moretó
AU  - Mohammad Zarrin
TI  - Influence of the number of Sylow subgroups on solvability of finite groups
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 1227
EP  - 1230
VL  - 358
IS  - 11-12
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.146
LA  - en
ID  - CRMATH_2020__358_11-12_1227_0
ER  - 
%0 Journal Article
%A Chimere Stanley Anabanti
%A Alexander Moretó
%A Mohammad Zarrin
%T Influence of the number of Sylow subgroups on solvability of finite groups
%J Comptes Rendus. Mathématique
%D 2020
%P 1227-1230
%V 358
%N 11-12
%I Académie des sciences, Paris
%R 10.5802/crmath.146
%G en
%F CRMATH_2020__358_11-12_1227_0
Chimere Stanley Anabanti; Alexander Moretó; Mohammad Zarrin. Influence of the number of Sylow subgroups on solvability of finite groups. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1227-1230. doi : 10.5802/crmath.146. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.146/

[1] Robert M. Guralnick Subgroups of prime power index in a simple group, J. Algebra, Volume 81 (1983), pp. 312-319 | MR | Zbl

[2] Marshal jun. Hall On the number of Sylow subgroups in a finite group, J. Algebra, Volume 73 (1967), pp. 363-371 | DOI | MR | Zbl

[3] Hans Kurzweil; Bernd Stellmacher The Theory of Finite Groups: An Introduction, Universitext, Springer, 2004 | Zbl

[4] Robert A. Liebler; Jay E. Yellen In search of non-solvable groups of central type, Pac. J. Math., Volume 82 (1979) no. 2, pp. 485-492 | DOI | Zbl

[5] Sajjad Mahmood Robati A solvability criterion for finite goups related to the number of Sylow subgroups, Commun. Algebra, Volume 48 (2020) no. 12, pp. 5176-5180 | DOI | MR | Zbl

[6] Michio Suzuki On a class of doubly transitive groups, Ann. Math., Volume 75 (1962), pp. 105-145 | DOI | MR | Zbl

[7] The GAP Group GAP – Groups, Algorithms, and Programming, 2019 (Version 4.10.2, https://www.gap-system.org)

[8] John G. Thompson Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Am. Math. Soc., Volume 74 (1968), pp. 383-437 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

A question of Malinowska on sizes of finite nonabelian simple groups in relation to involution sizes

Chimere Stanley Anabanti

C. R. Math (2020)