## Quotient Group

For a Group and a Normal Subgroup of , the quotient group of in , written and read  modulo '', is the set of Cosets of in . The elements of are written and form a Group under the normal operation on the group on the coefficient . Thus,

Since all elements of will appear in exactly one Coset of the Normal Subgroup , it follows that

where is the order of the group .

The slash Notation conflicts with that for a Field Extension, but the meaning can be determined based on context.

See also Abhyankar's Conjecture, Coset, Field Extension, Outer Automorphism Group, Normal Subgroup, Subgroup

References

Herstein, I. N. Topics in Algebra, 2nd ed. New York: Springer-Verlag, 1975.