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.
