A quotient group 
of 
by 
, where 
is a group and 
is a normal subgroup of
, is the set of cosets
of 
in 
. It is read "
modulo 
". 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.
