Abstract
We prove a structure theorem for a class of finite transitive permutation groups that arises in the study of finite bipartite vertex-transitive graphs. The class consists of all finite transitive permutation groups such that each non-trivial normal subgroup has at most two orbits, and at least one such subgroup is intransitive. The theorem is analogous to the O'Nan-Scott Theorem for finite primitive permutation groups, and this in turn is a refinement of the Baer Structure Theorem for finite primitive groups. An application is given for arc-transitive graphs.
Citation
Cheryl E. Praeger. "Finite transitive permutation groups and bipartite vertex-transitive graphs." Illinois J. Math. 47 (1-2) 461 - 475, Spring/Summer 2003. https://doi.org/10.1215/ijm/1258488166
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