For a group and a normal subgroup of , the quotient group of in , written and read " modulo ", is the set of cosets of in . Quotient groups are also called factor groups. 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 denotes the order of a group. This is also a consequence of Lagrange's group theorem with and
Although the slash notation conflicts with that for an extension field, the meaning can be determined based on context.