| 41. | All Abelian groups have only one-dimensional irreducible representations.
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| 42. | Let ? be a totally ordered abelian group.
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| 43. | There is a well-known notion for abelian groups.
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| 44. | Conversely, every periodic abelian group is locally finite.
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| 45. | Then G is a free abelian group ."
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| 46. | This turns the set into an abelian group.
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| 47. | Clearly, every finite abelian group is finitely generated.
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| 48. | What's the free ring over an abelian group?
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| 49. | Is a short exact sequence of abelian groups.
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| 50. | More generally, every finitely-generated free abelian group.
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