It is interesting in a group that conjugation $(x,y)\mapsto x^y:=y^{-1}xy$ behaves like exponentation among real numbers:

1. $(xy)^z=x^zy^z$
2. $(x^y)^z=x^{yz}$

That is, real numbers with multiplication and exponentation forms the same algebraic structure as a group with multiplication and conjugation Is there a name for this algebraic structure?