Does there exists a homomorphism from a finite abelian group G to R*(Set of reals under multiplication) ?
My try: Suppose f be non trivial homomorphism from G to R*. Since f(G) is subgroup of R* and G is finite implies R* has a finite subgroup which is other than non trivial. Now R* has only finite subgroup {1,-1} this implies f(G)= {1,-1} .Also from property of homomorphism order of f(G) divides order of G this will conclude that order of G is even. Now I am stuck after this.How to proceed?