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Prove that Z is isomorphic to the multiplicative group of all rational numbers of the

Chapter 18, Problem 18.1

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QUESTION:

Prove that Z is isomorphic to the multiplicative group of all rational numbers of the form2m (m E Z).

Questions & Answers

QUESTION:

Prove that Z is isomorphic to the multiplicative group of all rational numbers of the form2m (m E Z).

ANSWER:

Step 1 of 3

Consider the  is a subgroup of multiplicative group of non-zero rational.

                                                             

Define

                                                                   

 Such that

                                                                   

 

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