Exercise
Consider the set G of nonzero elements of the smallest subfield of a field R. They form a multiplicative group. Which statement about G is true for all R?
G is cyclic.
G is abelian.
G is finite.
G is not cyclic.
How about the case where G = Q\{0}?
Correct! G is abelian since R is commutative.
How about the case where G = Q\{0}?
How about the case where G = Z/3Z\{0}?