If is a free abelian group, and G is the subgroup with basis xaX X ' X x 0 for some x 0 X, then F G Zx o Generalize this result to arbitrary subsets X ' of X F zx Zx TEX...

ANSWER First we consider the case where X X x0 for some x0 X Let F xX ZE be the free abelian group w ...

If is a free abelian group, and G is the subgroup with basis xaX X' = X

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is a free abelian group, and G is the subgroup with basis xaX X' = X - {x₀} for some x₀ϵ X, then F/G ≅ Zx_o. Generalize this result to arbitrary subsets X' of X.

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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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If is a free abelian group, and G is the subgroup with basis xaX X' = X

Question:

F = Σzx Zx TEX

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ANSWER First we consider the case where X X x0 for some x0 X Let F xX ZE be the free abelian group w...View the full answer

Algebra Graduate Texts In Mathematics 73

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