On sharply edge-transitive permutation groups

Babai, László ; Cameron, Peter J. ; Deza, Michel ; Singhi, Navin M. (1981) On sharply edge-transitive permutation groups Journal of Algebra, 73 (2). pp. 573-585. ISSN 0021-8693

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Related URL: http://dx.doi.org/10.1016/0021-8693(81)90336-7


We consider the problem of determining the maximum possible out-degree d(n) of a digraph on n vertices which admits a sharply edge-transitive group. We show that d(n) ≥ cn/log log n for every n, while d(n)=(½)n infinitely often. Also, d(n)=n−1 if and only if n is a prime power, whereas for non-prime-power values of n, we show that n−d(n) tends to infinitely with n. The question has interesting group-theoretic aspects. This and related problems generalise the existence question for projective planes.

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