| 1. | The first two properties make a bilinear map of the abelian group.
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| 2. | This gave a finite abelian group, as was recognised at the time.
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| 3. | In principle, multiplicative quantum numbers can be defined for any abelian group.
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| 4. | Abelian groups of rank greater than 1 are sources of interesting examples.
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| 5. | This includes kernels for homomorphisms between abelian groups as a special case.
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| 6. | Rank of an abelian group is analogous to the order is finite.
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| 7. | There are five abelian groups corresponding to the five partitions of 4.
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| 8. | From the category of topological spaces to the category of abelian groups.
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| 9. | The functor which maps a ring to its underlying additive abelian group.
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| 10. | Free abelian groups have properties which make them similar to vector spaces.
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