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## Definition: Isomorphism

An isomorphism is a bijective homomorphism $$f:G\to H$$ of two algebraic structures $$(G,\ast)$$, $$(H,\cdot)$$

$f(a\ast b)=f(a)\cdot f(b).$

If an isomorphism exists between $$(G,\ast)$$, $$(H,\cdot),$$ we write $$G\simeq H$$ and say that $$G$$ and $$H$$ are isomorphic.

| | | | | created: 2014-02-23 22:26:59 | modified: 2019-02-10 14:39:37 | by: bookofproofs | references: [577]