Geodesic
OD-characterization of almost simple groups related to $L_{2}(49)$
Archivum mathematicum, Tome 44 (2008) no. 3, pp. 191-199 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group $L_{2}(49)$. As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to $L_{2}(49)$ except $L_{2}(49)\cdot 2^{2}$. Also, we prove that if $M$ is an almost simple group related to $L_{2}(49)$ except $L_{2}(49)\cdot 2^{2}$ and $G$ is a finite group such that $|G|=|M|$ and $\Gamma (G)=\Gamma (M)$, then $G\cong M$.
In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group $L_{2}(49)$. As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to $L_{2}(49)$ except $L_{2}(49)\cdot 2^{2}$. Also, we prove that if $M$ is an almost simple group related to $L_{2}(49)$ except $L_{2}(49)\cdot 2^{2}$ and $G$ is a finite group such that $|G|=|M|$ and $\Gamma (G)=\Gamma (M)$, then $G\cong M$.
Classification : 20D05, 20D06, 20D60
Keywords: almost simple group; prime graph; degree of a vertex; degree pattern 
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Zhang, Liangcai; Shi, Wujie. OD-characterization of almost simple groups related to $L_{2}(49)$. Archivum mathematicum, Tome 44 (2008) no. 3, pp. 191-199. http://geodesic.mathdoc.fr/item/ARM_2008_44_3_a2/

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