Question

From the additive group Q to which one of the following groups does there exist a non-trivial group homomorphism ?

• A. $\R^×$, the multiplicative group of non-zero real numbers
• B. $\Z$, the additive group of integers
• C. $\Z_2$, the additive group of integers modulo 2
• D. Q×, the multiplicative group of non-zero rational numbers

Answer 1

Answer: (A)

$\R^×$, the multiplicative group of non-zero real numbers

Answer 2

The correct option is (A) : $\R^×$, the multiplicative group of non-zero real numbers.