quotient group

Definition

Suppoose a normal subgroup $N$ of a group $N$, then, the set of cosets of $N$ is a group, called the quotient group, dennoted as $G/N$

Notes

• the elements of the quotient group are actually sets, or rather, they are cosets, rather than individual elements of $G$;
  • indeed, a law of composition may be defined on the set of cosets of a normal subgroup $N$ of any group $G$

See also

• subgroup

References

1. M. Artin, Algebra, 2. ed. Boston, Mass. Munich: Pearson Education, Prentice Hall, 2011, p. 66.
2. https://en.wikipedia.org/wiki/Quotient_group