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.
