If G is a finitely generated abelian group such that G /G t , has rank n,
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If G is a finitely generated abelian group such that G /Gt, has rank n, and H is a subgroup of G such that H/ Ht has rank n-m, then m ≤ n and (G/ H)/(G/ H)t has rank n - m.
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By the Second Isomorphism Theorem we have GH GHt GGt HHt GHt Gt H Note that GHt is a finitely ge...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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