Geodesic
Recognition of Finite Groups by the Prime Graph
Algebra i logika, Tome 45 (2006) no. 4, pp. 390-408

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We obtain the first example of an infinite series of finite simple groups that are uniquely determined by their prime graph in the class of all finite groups. We also show that there exist almost simple groups for which the number of finite groups with the same prime graph is equal to 2.
Keywords: prime graph, finite group, modular representations, recognition. 
@article{AL_2006_45_4_a1,
     author = {A. V. Zavarnitsin},
     title = {Recognition of {Finite} {Groups} by the {Prime} {Graph}},
     journal = {Algebra i logika},
     pages = {390--408},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_4_a1/}
}
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A. V. Zavarnitsin. Recognition of Finite Groups by the Prime Graph. Algebra i logika, Tome 45 (2006) no. 4, pp. 390-408. http://geodesic.mathdoc.fr/item/AL_2006_45_4_a1/