Let G, H, and K be finitely generated abelian groups. (a) If GG HH, then G
Question:
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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a If GG HH then G H This statement is true The key idea is that if two groups are isomorphic then th...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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