Cosets in Group Theory | Abstract Algebra

We introduce cosets of subgroups in groups, these are wonderful little discrete math structures, and we'll see coset examples and several coset theorems in this video. If H is a subgroup of a group G, and a is an element of G, then Ha is the set of all products ha where a is fixed and h ranges over H. Ha is called a left coset of H in G, and the right coset aH is defined similarly. We will see finite cosets and infinite cosets. #abstractalgebra #grouptheory

Cosets of a subgroup partition the whole group, and cosets with common elements are equal, we discuss both of these facts in this video, and we prove the latter fact. Our discussions of cosets will eventually lead to a proof of a famous result: Lagrange's Theorem.

Cosets of a Subgroup have the Same Size: (coming soon)
Proof that Cosets Partition the Group:    • Proof: Cosets Partition the Group | A...  
Lagrange's Theorem: (coming soon)

Abstract Algebra Course:    • Abstract Algebra  
Abstract Algebra Exercises:

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