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. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.
Read more about Group Isomorphism: Definition and Notation, Examples, Properties, Cyclic Groups, Consequences, Automorphisms
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—Babette Deutsch (1895–1982)