Quotient Groups and Homomorphic Images | Abstract Algebra

We introduce quotient groups/factor groups. The quotient group of a group G by a normal subgroup H is the set of all cosets of H in G with the operation of coset multiplication. We prove the quotient group construction is indeed a group, and that it is a homomorphic image of the containing group. Thus, quotient groups give us a way to construct homomorphic images of a group. #abstractalgebra #grouptheory

Normal Subgroups:    • Definition of Normal Subgroups | Abst...  
Left and Right Cosets in Normal Subgroups:    • Equivalent Definitions of Normal Subg...  
Coset Multiplication on Normal Subgroups:    • Coset Multiplication on Normal Subgro...  
Fundamental Homomorphism Theorem:    • Proving The Fundamental Homomorphism ...  

Abstract Algebra Course:    • Abstract Algebra  
Abstract Algebra Exercises:    • Abstract Algebra Exercises  

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