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Show that the group of positive rational numbers under
Chapter 4, Problem 37E(choose chapter or problem)
QUESTION:
Problem 37E
Show that the group of positive rational numbers under multiplication is not cyclic.
Questions & Answers
QUESTION:
Problem 37E
Show that the group of positive rational numbers under multiplication is not cyclic.
ANSWER:
Step 1 of 2
To prove that the group of positive rational numbers under multiplication is not cyclic.
If possible, let us assume that the group of positive rational number is cyclic.
Then, must have a generator other than the multiplicative identity.
Suppose, be a generator of the group such that . Then, every element of is some integer power of i.e.,