A group isomorphism is a bijective homomorphism between two groups, meaning it preserves the group operation and establishes a one-to-one correspondence between the elements of the groups. This concept reveals the structural similarities between groups, indicating that they are essentially the same from a group-theoretic perspective. When two groups are isomorphic, they exhibit the same algebraic structure, allowing mathematicians to treat them as indistinguishable for various theoretical purposes.
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