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.

What is isomorphic 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 properties are preserved by isomorphism?

An isomorphism preserves properties like the order of the group, whether the group is abelian or non-abelian, the number of elements of each order, etc. Two groups which differ in any of these properties are not isomorphic.