SOLVED:Show that any cyclic group is Abelian. Hint: Does a matrix commute with itself?

SOLVED: true or falsegive a brief justification or counterexample to support youranswerIf every proper subgroup of a group G is cyclic, then G is acyclic group.

SOLVED:Let G be a cyelie group, and f: G \rightarrow G^{\prime} a homomorphism. Show that the image of f is cyclic.

a. Show that a cyclic group of order 8 has a cyclic group of order 4 as a homomorphic image. b. Show that a cyclic group of order 6 has a cyclic group of order 2 as a homomorphic image. | Numerade

a. Show that a cyclic group of order 8 has a cyclic group of order 4 as a homomorphic image.b. Show that a cyclic group of order 6 has a cyclic group of order 2 as a homomorphic image.