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# Rational Numbers Under Addition and Multiplication

ABSALG-VX4L21

Let $({\mathbb Q}, +)$ be the group of rational numbers under addition.

Let $({\mathbb Q}^\ast, \times)$ be the group of non-zero rational numbers under multiplication.

Which of the following are TRUE?

Select ALL that apply.

A

$({\mathbb Q}, +)$ has no non-zero element of finite order.

B

$({\mathbb Q}, +)$ is finitely generated.

C

$({\mathbb Q}, +)$ is a free abelian group.

D

$({\mathbb Q}^\ast, \times)$ is a free abelian group.

E

$({\mathbb Q}^\ast, \times)$ has finite rank.