Collineations of V-Spaces

V-spaces are special non-planar ³-spaces in the sense of Betten. The group of collineations of a given V-space is a Lie group of dimension at least 4. We will determine all V-spaces with a large collineation group. If the V-space is generated by a function f, then dim 5 implies f(x)=c|x| ^p for some constants c>0, p>1.