isomorphism

Thus, there is only one group of order 15 (up to isomorphism).

But there is in general no natural isomorphism between these two spaces.

The object A itself is only unique up to isomorphism.

However, it is also true that yields a natural isomorphism from to itself.

It is worth noting that this will not, in general, be an isomorphism.

There are four isomorphism class of graphs, also shown at the right.

The isomorphism classes can be understood in a simpler way as well.

A theory is called categorical if it has only one model, up to isomorphism.

The (anti-) isomorphism is a particular natural one as will be described next.

Each factor has a standard representation, which is unique up to isomorphism.

We first state the three isomorphism theorems in the context of groups.

It is not hard to check that A is an isomorphism.

It was the realization of what he had described in 1946 as an "Isomorphism making machine".

Then and thus the result follows by use of the first isomorphism theorem.

Thus, the definition of an isomorphism is quite natural.

A named isomorphism indicates which features are selected for this purpose.

The bijection is then called the isomorphism of the graphs.

All complex tori, up to isomorphism, are obtained in this way.

However, the isomorphism is not natural, and depends on the choice of conjugation.

For example, "Up to isomorphism, there are eleven rings of order 4."

Every field with 'p' elements is isomorphism to this one.

The concept of a homomorphism and an isomorphism may be defined.

A related phenomenon is exceptional isomorphism, when two series are in general different, but agree for some small values.

There is an obvious order isomorphism between and for two finite sets with the same size.

Over the real numbers, there are two such Jordan algebras up to isomorphism.