Every cyclic group is a/an ______
A. infinite subgroup
B. abelian group
C. monoid
D. commutative semigroup
Answer:B
Every cyclic group is a/an ______
A. infinite subgroup B. abelian group C. monoid D. commutative semigroup
Explanation: Let C be a cyclic group with a generator g∈C. Namely, we have G={g.Let x and y be arbitrary elements in C. Then, there exists n, m∈Z such that x=gn and y=gm. It follows that x*y = gn*gm = gn+m = gm*gn = yx. Hence, we find that xy=yx for any x,y belongs to G.Thus, G is an abelian group.