Quotient Group
If , the quotient group is the group of cosets with .
Definition 7.5 (Quotient Group)
If , the group provided by Theorem 7.4 is called the quotient of by .
Examples
The quotient groups and are isomorphic to and the trivial group, respectively. For , . If , then and . In particular, .
Warning
Quotient groups do not generally undo direct products. For example, and , although because is cyclic and is not.
Related
Stated in
- Definition 7.5 (Quotient Group)§7.2 Quotient Groups