Characterizing finite locally s-arc transitive graphs with a star normal quotient

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Abstract

Let Gamma be a finite locally (G, s)-arc transitive graph with s >= 2 such that G is intransitive on vertices. Then G is bipartite and the two parts of the bipartition are G-orbits. In previous work the authors showed that if G has a non-trivial normal subgroup intransitive on both of the vertex orbits of G, then Gamma is a cover of a smaller locally s-arc transitive graph. Thus the 'basic' graphs to study are those for which G acts quasiprimitively on at least one of the two orbits. In this paper we investigate the case where G is quasiprimitive on only one of the two G-orbits. Such graphs have a normal quotient which is a star. We construct several infinite families of locally 3-arc transitive graphs and prove characterization results for several of the possible quasiprimitive types for G.
Original languageEnglish
Pages (from-to)641-658
JournalJournal of Group Theory
Volume9
Issue number5
DOIs
Publication statusPublished - 2006

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