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