A note on automorphism groups of symmetric cubic graphs. (English) Zbl 07474441
Summary: We study \(s\)-arc-transitive cubic graph \(\Gamma\), and give a characterization of minimal normal subgroups of the automorphism group. In particular, each \(\Gamma\) with quasi-primitive automorphism group is characterized. An interesting consequence of this characterization states that a non-solvable minimal normal subgroup \(M\) contains at most 2 copies of non-abelian simple group when it acts transitively on arcs, or contains at most 6 copies of non-abelian simple group when it acts regularly on vertices.
MSC:
| 20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
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