Group Isomorphism
Group isomorphism is a concept in abstract algebra that describes a relationship between two groups. Two groups, G and H, are said to be isomorphic if there exists a bijective function (one-to-one and onto) between them that preserves the group operation. This means that the structure of the groups is essentially the same, even if their elements and operations appear different.
When two groups are isomorphic, they can be thought of as different representations of the same mathematical object. For example, the group of integers under addition and the group of even integers under addition are isomorphic, as they share the same structure despite having different elements. This concept helps mathematicians understand the fundamental properties of groups without getting bogged down in their specific details.