| 31. | However, associativity and being an abelian group are universal properties.
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| 32. | This gives a contravariant functor from manifolds to abelian groups.
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| 33. | Finitely generated abelian groups are completely classified and are particularly easy to work with.
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| 34. | This follows from the classification of finitely generated abelian groups.
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| 35. | The restrictions that define an abelian group may be removed in different orders also.
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| 36. | It can readily be generalized to an arbitrary non-Abelian group.
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| 37. | These groups are our first examples of infinite non-abelian groups.
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| 38. | One starts with the notion of an abelian group.
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| 39. | And takes chain maps to maps of abelian groups.
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| 40. | Let G be a locally compact, abelian group.
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