Sharp three-transitivity
= Sharp three-transitivity
{title2=$|G|=n(n-1)(n-2)$}
= Sharply three-transitive
{synonym}
Exactly one element sends each ordered triple of distinct points to each other such triple. On a <projective line>, representatives of the first two target points form a <basis>; scaling them so their sum represents the third point gives the unique projective transformation.