On Groups of Degree N AND n −1, and Highly‐Symmetric Edge Colourings

It is known that, if G is a triply transitive permutation group on a finite set X with a regular normal subgroup N, then |N| = 2 (d ̂ 2) or |N| = 3. (See [12; Theorem 11.3].) If N is a regular normal subgroup of a permutation group G on X, xeX, and Gx is the stabiliser of x, then Gx £ G/JV (as abstract group), and so G has a representation on a set Y such that, for xeX, the representations of Gx on X {*} and Y are equivalent. I show that, with this hypothesis replacing the existence of a regular normal subgroup of a triply transitive group, only one further situation arises: