(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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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Question Posted:
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