Geodesic
A characterization of the simple sporadic groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 200-204.

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Let $G$ be a finite group, $n_{p}(G)$ be the number of Sylow $p$–subgroup of $G$ and $t(2, G)$ be the maximal number of vertices in cocliques of the prime graph of $G$ containing 2. In this paper we prove that if $G$ is a centerless group with $t(2,G)\geq 2$ and $n_{p}(G)$=$n_{p}(S)$ for every prime $p\in \pi (G)$, where $S$ is the sporadic simple groups, then $S\leq G\leq $Aut$(S)$.
Keywords: Finite Group, Sylow subgroup.
Mots-clés : simple group 
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A. K. Asboei. A characterization of the simple sporadic groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 200-204. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a7/

[1] A. K. Asboei, S. S. Amiri, A. Iranmanesh, A. Tehranian, “A characterization of some linear groups by the number of Sylow subgroups”, Aust. J. Basic and Appl. Sci., 5 (2011), 831–834

[2] A. K. Asboei, A new characterization for some linear groups by the number of sylow subgroups, unpublished | Zbl

[3] A. K. Asboei, S. S. Amiri, A. Iranmanesh, A. Tehranian, “A New Characterization of the Mathieu Groups of degree 11 and 12 by the Number of Sylow Subgroups”, Bol. Soc. Paran. Mat., 31 (2013), 213–218 | MR

[4] A. S. Kondratiev, “Prime graph components of finite simple groups”, Math. USSR-Sb., 67 (1990), 235–247 | DOI | MR

[5] A. V. Vasiliev, E. P. Vdovin, “An adjacency criterion for the prime graph of a finite simple group”, Algebra and Logic, 44 (2005), 381–406 | DOI | MR | Zbl

[6] A. V. Vasiliev, “On connection between the structure of finite group and properties of its prime graph”, Siberian Math. J., 46 (2005), 396–404 | DOI | MR | Zbl

[7] A. V. Zavarnitsine, “Finite simple groups with narrow prime spectrum”, Siberian Electronic Math. Reports, 6 (2009), 1–12 | MR

[8] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite Groups, Clarendon, Oxford, 1985 | MR | Zbl

[9] J. S. Williams, “Prime graph components of finite groups”, J. Algebra, 69 (1981), 487–513 | DOI | MR | Zbl

[10] J. Zhang, “Sylow numbers of finite groups”, J. Algebra, 176 (1995), 111–123 | DOI | MR | Zbl

[11] M. Hall, The Theory of Groups, Macmillan, New York, 1959 | MR | Zbl