Because an isomorphism preserves some structural aspect of a set or mathematical group, it is often used to map a complicated set onto a simpler or better-known set in order to establish the original set's properties. Isomorphisms are one of the subjects studied in group theory.

What is isomorphism function?

In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called isomorphic.

What makes an isomorphism?

Definition 1 (Isomorphism of vector spaces). Two vector spaces V and W over the same field F are isomorphic if there is a bijection T : V → W which preserves addition and scalar multiplication, that is, for all vectors u and v in V , and all scalars c ∈ F, T(u + v) = T(u) + T(v) and T(cv) = cT(v).