Show that Q under addition is not a free abelian group.

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A First Course In Abstract Algebra

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Authors: John Fraleigh

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Question Posted: Jan 09, 2023 08:34 AM

How many different homomorphisms are there of a free abelian group of rank 2 onto a. Z 4 ? b. Z 6 ? c. S 3 ?
How many different homomorphisms are there of a free abelian group of rank 2 into a. Z 4 ? b. Z 6 ? c. S 3 ?
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Show that Q under addition is not a free abelian group.

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Because Q is not cyclic any basis for Q must contain at ...View the full answer

A First Course In Abstract Algebra

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