Geodesic
On recognizability of some finite simple orthogonal groups by spectrum
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 30-43

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It is proved that if $G$ is a finite group with the same set of element orders as simple group $D_p(q)$, where $p$ is a prime, $p\ge5$ and $q\in\{2,3,5\}$, then the commutator group of $G/F(G)$ is isomorphic to $D_p(q)$, the subgroup $F(G)$ is equal to 1 for $q=5$ and to $O_q(G)$ for $q\in\{2,3\}$, $F(G)\le G'$ and $|G/G'|\le2$.
Keywords: finite simple group, spectrum of a group, prime graph, recognition by spectrum
Mots-clés : orthogonal group. 
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O. A. Alekseeva; A. S. Kondrat'ev. On recognizability of some finite simple orthogonal groups by spectrum. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 30-43. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a2/