S-Arc-transitive graphs and normal subgroups

Cai-Heng Li; A. Seress; Shu-Jiao Song

doi:10.1016/j.jalgebra.2014.08.032

S-Arc-transitive graphs and normal subgroups

Cai-Heng Li, A. Seress, Shu-Jiao Song

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Abstract

© 2014 Elsevier Inc. We study s-arc-transitive graphs with s≥. 2, and give a characterisation of the actions of vertex-transitive normal subgroups. An interesting consequence of this characterisation states that each non-bipartite 3-arc-transitive graph is a normal cover of a 2-arc-transitive graph admitting a simple group, or a locally primitive graph admitting a simple group with a soluble vertex stabiliser.

Original language	English
Pages (from-to)	331-348
Number of pages	18
Journal	Journal of Algebra
Volume	421
DOIs	https://doi.org/10.1016/j.jalgebra.2014.08.032
Publication status	Published - 1 Jan 2015

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title = "S-Arc-transitive graphs and normal subgroups",

abstract = "{\textcopyright} 2014 Elsevier Inc. We study s-arc-transitive graphs with s≥. 2, and give a characterisation of the actions of vertex-transitive normal subgroups. An interesting consequence of this characterisation states that each non-bipartite 3-arc-transitive graph is a normal cover of a 2-arc-transitive graph admitting a simple group, or a locally primitive graph admitting a simple group with a soluble vertex stabiliser.",

author = "Cai-Heng Li and A. Seress and Shu-Jiao Song",

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AU - Li, Cai-Heng

AU - Seress, A.

AU - Song, Shu-Jiao

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N2 - © 2014 Elsevier Inc. We study s-arc-transitive graphs with s≥. 2, and give a characterisation of the actions of vertex-transitive normal subgroups. An interesting consequence of this characterisation states that each non-bipartite 3-arc-transitive graph is a normal cover of a 2-arc-transitive graph admitting a simple group, or a locally primitive graph admitting a simple group with a soluble vertex stabiliser.

AB - © 2014 Elsevier Inc. We study s-arc-transitive graphs with s≥. 2, and give a characterisation of the actions of vertex-transitive normal subgroups. An interesting consequence of this characterisation states that each non-bipartite 3-arc-transitive graph is a normal cover of a 2-arc-transitive graph admitting a simple group, or a locally primitive graph admitting a simple group with a soluble vertex stabiliser.

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DO - 10.1016/j.jalgebra.2014.08.032

M3 - Article

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VL - 421

SP - 331

EP - 348

JO - Journal of Algebra

JF - Journal of Algebra

ER -

S-Arc-transitive graphs and normal subgroups

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