Geodesic
On the existence of Carter subgroups
Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 79-88

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In terms of normal series of a finite group, the existence criterion of a Carter subgroup is obtained. An example showing that the criterion cannot be reformulated in terms of composition factors is given. In conclusion, Carter subgroups in almost simple groups are classified. 
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E. P. Vdovin. On the existence of Carter subgroups. Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 79-88. http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a4/