Answer to Question #302692 in Abstract Algebra for prakash negi

Question

Let G be multiplication group all positive real number and R the additive group of all real number. Is G a subgroup of R? explain

Answer 1

A subgroup of a group G is a subset H of G that is a group with the same operation as on the group G. Since the operation of multiplication is different from the operation of addition, we conclude that G is not a subgroup of R.