(a) Show that the additive group of rationals Q is not finitely generated. (b) Show that Q...

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(a) Show that the additive group of rationals Q is not finitely generated.
(b) Show that Q is not free.
(c) Conclude that Exercise 9 is false if the hypothesis "finitely generated" is omitted.

Data from Exercise 9

Let G be a finitely generated abelian group in which no element (except 0) has finite order. Then G is a free abelian group.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:51 AM

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(a) Show that the additive group of rationals Q is not finitely generated. (b) Show that Q...

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a To show that Q is not finitely generated we assume that Q is finitely generated by some elements a...View the full answer

Algebra Graduate Texts In Mathematics 73

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