Referring the groups of automorphisms (holomorphic bijections) of the respective domains.

This is a homework problem. Is a basic course, so sophisticated answers may not be of help (it has a simple solution according to my teacher). Also, it looks like an Algebra problem, but I’ve been assured that there is a solution within complex analysis, so if anyone can give a non algebraic proof, it will be appreciated. I tried constructing a conformal mapping (between two of the domains) using a supposed isomorphism, also calculate the unit roots (of second degree, and some of higher degree) in each of the groups, and a couple ideas more, but with no luck. 
Thanks in advance for your help (and sorry about my poor English).

Edit:The question was edited to avoid sophisticated algebraic answers. Please, just use the very basic of algebra in your solution. Is a complex analysis exercise! (of course, if you just want to share a sohpisticated answer that can help other users, welcome.)