Question

Group Theory. G is the set of real numbers with the operation x*y=x+y+1. Find an isomorphism: f: R->G and show that it is an isomorphism.

Answer 1

Group Theory. Let a and b be elements of a group G. Let ord(a)=m and ord(b)=n. prove that if m and n are relatively prime, then no power of a can be equal to any power of b (except for e).

In doing this proof, i used the fact that m cannot divide n and n cannot divide m, hence they have no common divisors. therefore m cannot equal n. but i feel like i am missing something. Any help would be appreciated.