and Applied Analysis 3 Proof. This can be proved by induction on order ofG as follows. The first step of the induction is obvious since the only group of order 2 is Z2. Let G be a finite Abelian group and g ∈ G where g / e. If G is not a cyclic group, then there is a subgroup H which does not contain g, so a is a nontrivial homogenous element of the induced… (More)