Geodesic
Stabilizers of vertices of graphs with primitive automorphism groups and a strong version of the Sims conjecture. III
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 163-172 Cet article a éte moissonné depuis la source Math-Net.Ru

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This is the third in a series of papers whose results imply the validity of a strengthened version of the Sims conjecture on finite primitive permutation groups. In this paper, the case of primitive groups with simple socle of classical non-orthogonal Lie type and non-parabolic point stabilizer is considered.
Keywords: finite primitive permutation group, almost simple group, group of classical Lie type, stabilizer of a point, 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. III. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 163-172. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a15/

[1] Kondratev A.S., “Normalizatory silovskikh 2-podgrupp v konechnykh prostykh gruppakh”, Matem. zametki, 78:3 (2005), 368–376 | DOI | MR | Zbl

[2] Kondratev A.S., Trofimov V.I., “Stabilizatory vershin grafov i usilennaya versiya gipotezy Simsa”, Dokl. AN, 364:6 (1999), 741–743 | MR | Zbl

[3] Kondratev A.S., Trofimov V.I., “Stabilizatory vershin grafov s primitivnymi gruppami avtomorfizmov i usilennaya versiya gipotezy Simsa. I”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:4 (2014), 143–152 ; “Стабилизаторы вершин графов с примитивными группами автоморфизмов и усиленная версия гипотезы Симса. II”, 22:2 (2016), 177–187 | MR | MR

[4] Aschbacher M., “On the maximal subgroups of the finite classical groups”, Invent. Math., 76:3 (1984), 469–514 | DOI | MR | Zbl

[5] J.H. Conway [et. al.], Atlas of finite groups, Clarendon Press, Oxford, 1985, 252 pp. | MR | Zbl

[6] Bray J.N., Holt D.F., Roney-Dougal C.M., The maximal subgroups of the low-dimensional finite classical groups, London Math. Soc. Lect. Note Ser., 407, Cambridge University Press, Cambridge, 2013, 438 pp. | MR | Zbl

[7] Carter R.W., Simple groups of Lie type, Wiley, London, 1972, 331 pp. | MR | Zbl

[8] Gerono G.C., “Note sur la r$\acute{e}$solution en nombres entiers et positifs de l'équation $x^m=y^n+1$”, Nouv. Ann. Math. (2), 9 (1870), 469–471

[9] Gorenstein D., Finite groups, Harper and Row, N. Y., 1968, 528 pp. | MR | Zbl

[10] Gorenstein D., Harada R., “On finite groups with Sylow 2-subgroups of type $A_n$, $n=8,9,10,11$”, Math. Z., 117:1–4 (1970), 207–238 | DOI | MR | Zbl

[11] Gorenstein D., Lyons R., Solomon R., The classification of the finite simple groups. Number 3. Part I, v. 40, Math. Surveys Monogr., no. 3, Amer. Math. Soc., Providence, 1998, 420 pp.

[12] Kleidman P.B., Liebeck M.W., The subgroup structure of the finite classical groups, London Math. Soc. Lect. Note Ser., 129, Cambridge University Press, Sambridge, 1990, 304 pp. | MR | Zbl

[13] Mason D., “Finite simple groups with Sylow 2-subgroups of type $\mathrm{PSL}(4, q)$”, J. Algebra, 26:1 (1973), 75–97 | DOI | MR | Zbl

[14] Zsigmondy K., “Zur Theorie der Potenzreste”, Monatsh. Math. Phys., 3 (1892), 265–284 | DOI | MR | Zbl