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 language | English |
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Pages (from-to) | 641-658 |
Journal | Journal of Group Theory |
Volume | 9 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2006 |