Abstract
The result of the title is proved, assuming the truth of Sims’ conjecture on primitive permutation groups (which has recently been established using the classification of finite simple groups). An alternative approach to this result, using less group theory but relying on a theorem of Macpherson on infinite distance-transitive graphs, is explored.
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Cameron, P.J. There are only finitely many finite distance-transitive graphs of given valency greater than two. Combinatorica 2, 9–13 (1982). https://doi.org/10.1007/BF02579277
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DOI: https://doi.org/10.1007/BF02579277