Graphs with projective suborbits. Exceptional cases of characteristic~2.~I
Izvestiya. Mathematics , Tome 62 (1998) no. 6, pp. 1221-1279.

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This paper is the first of a series where we complete the description of finite vertex stabilizers for connected graphs with projective suborbits and, as a corollary, of vertex stabilizers for finite connected graphs in groups of automorphisms that act transitively on 2-arcs. In this part we complete the treatment of the case when the group acts transitively on 3-arcs.
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V. I. Trofimov. Graphs with projective suborbits. Exceptional cases of characteristic~2.~I. Izvestiya. Mathematics , Tome 62 (1998) no. 6, pp. 1221-1279. http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a7/

[1] Trofimov V. I., “Stabilizatory vershin grafov s proektivnymi podorbitami”, DAN SSSR, 315:3 (1990), 544–546 | MR | Zbl

[2] Trofimov V. I., “Grafy s proektivnymi podorbitami”, Izv. AN SSSR. Ser. matem., 55:4 (1991), 890–916 | MR

[3] Trofimov V. I., “Grafy s proektivnymi podorbitami. Sluchai malykh kharakteristik. I; II”, Izv. RAN. Ser. matem., 58:5 (1994), 124–171 | MR | Zbl

[4] Cameron P. J., “Finite permutation groups and finite simple groups”, Bull. London Math. Soc., 13 (1981), 1–22 | DOI | MR | Zbl

[5] Gardiner A., “Arc transitivity in graphs”, Quart. J. Math (2), 24 (1973), 399–407 | DOI | MR | Zbl

[6] Weiss R., “An application of p-factorization methods to symmetric graphs”, Math. Proc. Cambridge Phil. Soc., 85 (1979), 43–48 | DOI | MR | Zbl

[7] Delgado A., Stellmacher B., “Weak $(B,N)$-pairs of rank 2”, Groups and Graphs: New Results and Methods, Birkhäuser, Basel e.a., 1985, 58–244 | MR

[8] Weiss R., “Groups with a $(B,N)$-pair and locally transitive graphs”, Nagoya Math. J., 74 (1979), 1–21 | MR | Zbl

[9] Trofimov V. I., “More on the vertex stabilizers of the symmetric graphs with projective subconstituents”, Intern. Conf. Algebr. Combin., Abstracts, Vladimir, 1991, 36–37 | MR

[10] Timmesfeld F., Amalgams with rank 2 groups of Lie-type in characteristic 2, Preprint, Giessen Math. Inst. Univ., Justus–Liebig, 1984 | MR | Zbl

[11] Meierfrankenfeld U., Stellmacher B., “Pushing up weak $BN$-pairs of rank two”, Commun. Algebra, 21 (1993), 825–934 | DOI | MR | Zbl

[12] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A., ATLAS of finite groups, Oxford Univ. Press., Oxford e.a., 1985 | MR | Zbl

[13] Weiss R., “Graphs which are locally Grassmann”, Math. Ann., 297 (1993), 325–334 | DOI | MR | Zbl

[14] Trofimov V. I., Weiss R. M., “Graphs with a locally linear group of automorphisms”, Math. Proc. Cambridge Phil. Soc., 118:2 (1995), 191–206 | DOI | MR | Zbl

[15] Trofimov V. I., “Pismo v redaktsiyu”, Izv. RAN. Ser. matem., 59:4 (1995), 221 | MR

[16] Meixner T., “Failure of factorization modules for Lie-type groups in odd characteristic”, Commun. Algebra, 19 (1991), 3193–3222 | DOI | MR | Zbl

[17] Niles R., “Pushing-up in finite groups”, J. Algebra, 57 (1979), 26–63 | DOI | MR | Zbl

[18] McLaughlin J., “Some groups generated by transvections”, Arch. Math., 18 (1967), 364–368 | DOI | MR | Zbl

[19] McLaughlin J., “Some subgroup of $\operatorname {SL}_n(F_2)$”, Ill. J. Math., 13 (1969), 108–115 | MR | Zbl