Let G, H, and K be finitely generated abelian groups (a) If GG HH, then G H (b) If GH GK, then H K (c) If G 1 is a free abelian group of rank N 0 , then G 1 ZZ G 1 Z, but ZZ Z ...

a If GG HH then G H This statement is true The key idea is that if two groups are isomorphic then th ...

Let G, H, and K be finitely generated abelian groups. (a) If GG HH, then G

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Let G, H, and K be finitely generated abelian groups.
(a) If G⊕G ≅ H⊕H, then G ≅ H.
(b) If G⊕H ≅ G⊕K, then H ≅ K.
(c) If G₁ is a free abelian group of rank N₀ , then G₁⊕ Z⊕Z ≅ G₁⊕Z, but Z⊕Z ≅ Z.

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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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Let G, H, and K be finitely generated abelian groups. (a) If GG HH, then G

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Algebra Graduate Texts In Mathematics 73

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