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 $G\cong M$.
@article{119758,
author = {Liang Cai Zhang and Wu Jie Shi},
title = {OD-characterization of almost simple groups related to $L\_{2}(49)$},
journal = {Archivum Mathematicum},
volume = {044},
year = {2008},
pages = {191-199},
zbl = {1204.20006},
mrnumber = {2462974},
language = {en},
url = {http://dml.mathdoc.fr/item/119758}
}
Zhang, Liang Cai; Shi, Wu Jie. OD-characterization of almost simple groups related to $L_{2}(49)$. Archivum Mathematicum, Tome 044 (2008) pp. 191-199. http://gdmltest.u-ga.fr/item/119758/
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