An important example is a quotient group of a group.

Together, these equivalence classes are the elements of a quotient group.

The quotient group is called the mapping class group of X.

As a result, it gives a corresponding automorphism for every quotient group.

Since S is a simple group, its only quotient groups are itself and the trivial group.

Hence every class of the quotient group has precisely one reduced divisor.

Like the case of a quotient group, there is a canonical map given by .

One also says that the latter is a quotient group of the former, because some once different elements become equal in the new group.

It is the same construction used for quotient groups and quotient rings.

Namely, one has to take subgroups and quotient groups into account:

The reason G/N is called a quotient group comes from division of integers.

Moreover, every cyclically ordered group can be expressed as such a quotient group.

If the quotient group is torsion-free, the subgroup is pure.

Every quotient group of a powerful p-group is powerful.

Much of the importance of quotient groups is derived from their relation to homomorphisms.

This has the intuitive meaning that the images of "x" and "y" are supposed to be equal in the quotient group.

Note that the slash (/) denotes here quotient group.

Then, a factor of automorphy for corresponds to a line bundle on the quotient group .

The finite quotient group is precisely the automorphism group.

The quotient group is isomorphic to S (the symmetric group on 3 letters).

For sets, it usually means modulo (quotient group).

This turns the set of cosets into a group called the quotient group G/N.

The notion is similar to that of a quotient group or quotient space, but in the categorical setting.

The quotient group G / A is isomorphic with C.

The Iterated monodromy group of f is the following quotient group: