Two local conditions on the vertex stabiliser of arc-transitive graphs and their effect on the Sylow subgroups

DOI10.1515/JGT.2011.097zbMath1241.05046arXiv1102.4421MaRDI QIDQ2882895

Pablo Spiga

Publication date: 11 May 2012

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.4421

zbMATH Keywords

\(G\)-arc-transitive graphs

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (14)

A theory of semiprimitive groups ⋮ Constructing half-arc-transitive graphs of valency four with prescribed vertex stabilizers ⋮ A class of semiprimitive groups that are graph-restrictive ⋮ Bounds on the diameter of Cayley graphs of the symmetric group ⋮ On graph-restrictive permutation groups ⋮ On orders of automorphisms of vertex-transitive graphs ⋮ Vertex-transitive graphs with local action the symmetric group on ordered pairs ⋮ On locally semiprimitive graphs and a theorem of Weiss ⋮ An application of the Local C(G,T) Theorem to a conjecture of Weiss ⋮ Graphs with automorphism groups admitting composition factors of bounded rank ⋮ Non-expander Cayley Graphs of Simple Groups ⋮ Growth in groups: ideas and perspectives ⋮ Locally bi-2-transitive graphs and cycle-regular graphs, and the answer to a 2001 problem posed by Fouquet and Hahn ⋮ On the order of Borel subgroups of group amalgams and an application to locally-transitive graphs.

Cites Work

• On groups with every normal subgroup transitive or semiregular.
• Vertex-transitive graphs
• Graphs and finite permutation groups
• On the point stabilizer in a primitive permutation group.
• On the Sims Conjecture and Distance Transitive Graphs
• Elations of graphs
• THOMPSON–WIELANDT-LIKE THEOREMS REVISITED
• ARC TRANSITIVITY IN GRAPHS
• Collapsing permutation groups.

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