11. The number of independent generators is the rank of an abelian group . 12. For abelian groups , left cosets and right cosets are always the same. 13. This thesis set the road for his contributions on abelian groups . 14. Important technical tools used in classification of infinite abelian groups are basic subgroups. 15. This is a key step in the classification of finitely generated abelian groups . 16. Consider the category " D " of homomorphisms of abelian groups . 17. The quaternion group is the smallest example of nilpotent non-abelian group . 18. This construction makes simplicial homology a functor from simplicial complexes to abelian groups . 19. Let and be the complex Abelian groups formed by the symmetries and respectively. 20. By contrast, classification of general infinitely generated abelian groups is far from complete.
