Geodesic
Half-Transitive Automorphism Groups
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1243-1250

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a finite group and A a group of automorphisms of G. Clearly A acts as a permutation group on G#, the set of non-identity elements of G. We assume that this permutation representation is half transitive, that is all the orbits have the same size. A special case of this occurs when A acts fixed point free on G. In this paper we study the remaining or non-fixed point free cases. We show first that G must be an elementary abelian g-group for some prime q and that A acts irreducibly on G. Then we classify all such occurrences in which A is a p-group. 
Isaacs, I. M.; Passman, D. S. Half-Transitive Automorphism Groups. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1243-1250. doi: 10.4153/CJM-1966-122-5
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