Is the set of dilations a group? More specifically, is the set of dilations closed under composition?

Answer 1

Yes, probably. Like #1 I wonder, in what context. But if it is dilations of Rn, n dimensional Euclidean space, then G={all functions f:Rn -> Rn such that f(x)=alpha*x for positive real alpha} would be the group and then:
closed: a1*(a2*x) = (a1*a2)*x
associative: check... a1*((a2*a3)*x)) = (a1*a2)*(a3*x)
identity id(x)=1*x check
inverse (1/a1)*x
it is also a communitative group: a1*a2 = a2*a1
<<< all those x's should be vectors x in Rn ..........
The word "dilations" usually includes compressions, 0

Answer 2

What the context? What's a dilation?