Order of Cosets Equals Order of Subgroup | Abstract Algebra

We prove that for a group G and a subgroup H, every coset Ha of H has the same order as H, and thus all the cosets of the subgroup H have the same order as each other. This is our final step to prove Lagrange's Theorem, which states for a finite group G and subgroup H, the order of G is a multiple of the order of H. We will discuss this theorem further in the next lesson. #abstractalgebra #grouptheory

Intro to Cosets in Group Theory:    • Cosets in Group Theory | Abstract Alg...  
Proof Cosets Partition the Group:    • Proof: Cosets Partition the Group | A...  

Abstract Algebra Course:    • Abstract Algebra  
Abstract Algebra Exercises:

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