Geodesic
Stabilizers of vertices of graphs with primitive automorphism groups and a~strong version of the Sims conjecture.~I
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 143-152

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This is the first in a series of papers whose results imply the validity of a strong version of the Sims conjecture on finite primitive permutation groups from the authors' article “Stabilizers of graph's vertices and a strengthened version of the Sims conjecture”, Dokl. Math. 59(1), 113–115 (1999). In this paper, the case of non almost simple primitive groups and the case of primitive groups with alternating socle are considered.
Keywords: finite primitive permutation group, stabilizer of point, graph, the Sims conjecture. 
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A. S. Kondrat'ev; V. I. Trofimov. Stabilizers of vertices of graphs with primitive automorphism groups and a~strong version of the Sims conjecture.~I. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 143-152. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a12/