Show that a finite abelian group is not cyclic if and only if it contains a subgroup

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Show that a finite abelian group is not cyclic if and only if it contains a subgroup isomorphic to Z_p x Z_pfor some prime p.

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 05, 2023 05:27 AM

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Show that a finite abelian group is not cyclic if and only if it contains a subgroup

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Recall that every subgroup of a cyclic group is cyclic Thus if a finite abelian group G contain...View the full answer

A First Course In Abstract Algebra

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