Abstract:
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.
This publication is cited in the following 15 articles:
Pablo Spiga, “An overview on vertex stabilizers in vertex-transitive graphs”, Boll Unione Mat Ital, 2024
V. I. Trofimov, “A Graph with a Locally Projective Vertex-Transitive Group of Automorphisms Aut(Fi22) Which Has a Nontrivial Stabilizer of a Ball of Radius 2”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S300–S304
Spiga P., “An Application of the Local C(G, T) Theorem To a Conjecture of Weiss”, Bull. London Math. Soc., 48:1 (2016), 12–18
Guo S. Li Ya. Hua X., “(G,s)-Transitive Graphs of Valency 7”, Algebr. Colloq., 23:3 (2016), 493–500
M. Giudici, L. Morgan, “A class of semiprimitive groups that are graph-restrictive”, Bulletin of the London Mathematical Society, 2014
C.H.eng Li, Ákos Seress, Sh.J.iao Song, “s-Arc-transitive graphs and normal subgroups”, Journal of Algebra, 2014
Cai Heng Li, Hua Zhang, “On Finite 2-Path-Transitive Graphs”, J. Graph Theory, 2012, n/a
Praeger Ch.E. Spiga P. Verret G., “Bounding the Size of a Vertex-Stabiliser in a Finite Vertex-Transitive Graph”, J. Comb. Theory Ser. B, 102:3 (2012), 797–819
Spiga P., “On G-locally primitive graphs of locally Twisted Wreath type and a conjecture of Weiss”, J Combin Theory Ser A, 118:8 (2011), 2257–2260
Trofimov V.I., Weiss R.M., “The group E-6(q) and graphs with a locally linear group of automorphisms”, Mathematical Proceedings of the Cambridge Philosophical Society, 148:Part 1 (2010), 1–32
Trofimov V.I., “Supplement to “The group E-6(q) and graphs with a locally linear group of automorphisms” by V. I. Trofimov and R. M. Weiss”, Mathematical Proceedings of the Cambridge Philosophical Society, 148:Part 1 (2010), 33–45
Ivanov A.A., Shpectorov S.V., “Amalgams determined by locally projective actions”, Nagoya Mathematical Journal, 176 (2004), 19–98
V. I. Trofimov, “Graphs with projective suborbits. Exceptional cases of characteristic 2. IV”, Izv. Math., 67:6 (2003), 1267–1294
V. I. Trofimov, “Graphs with projective suborbits. Exceptional cases of characteristic 2. III”, Izv. Math., 65:4 (2001), 787–822
V. I. Trofimov, “Graphs with projective suborbits. Exceptional cases of characteristic 2. II”, Izv. Math., 64:1 (2000), 173–192
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