| 11. | Once the machinery of quotient groups is built up the need for them seems to disappear.
|
| 12. | Both the subgroup and the quotient group are isomorphic with "'Z "'2.
|
| 13. | Much of the importance of quotient groups is derived from their relation to kernel of " ? ".
|
| 14. | These are not finite themselves, but each contains a abelian subgroup such that the corresponding quotient group is finite.
|
| 15. | The quotient group is isomorphic to " S " 3 ( the symmetric group on 3 letters ).
|
| 16. | Since " S " is a simple group, its only quotient groups are itself and the trivial group.
|
| 17. | The rank " n " cohomology group is the quotient group of the closed forms by the exact forms.
|
| 18. | Let denote the subgroup of generated by, since, it is a normal subgroup and one may take the quotient group.
|
| 19. | Then, a factor of automorphy for \ Gamma corresponds to a line bundle on the quotient group G / \ Gamma.
|
| 20. | In this case, the set of all cosets form a group called the quotient group with the operation " defined by.
|
