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OD-characterization of almost simple groups related to $L_{2} (49)$

Liang Cai Zhang, Wu Jie Shi (2008)

Archivum Mathematicum

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 $Γ (G) = Γ (M)$ , then $G ≅ M$ .

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OD-characterization of almost simple groups related to $L_{2} (49)$

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On groups admitting a group of automorphisms whose centralizer has bounded rank.

On groups of odd order admitting an elementary 2-group of automorphisms

On Groups of Squarefree Order.

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