Quotient groups

Cosets of a normal subgroup inherit a well-defined group operation.

Different ways to understand it

No reviewed video yet. Explore the concept in a map or suggest a resource. Suggest a video

Group homomorphisms
A homomorphism preserves group multiplication; its kernel measures failure of injectivity.
Normal subgroups
A subgroup invariant under conjugation allows consistent multiplication of cosets.
Subgroups
A subgroup is a subset that forms a group under the inherited operation.
Binary operations
A binary operation combines two elements into one in a specified set.
Cosets and Lagrange's theorem
Cosets partition a finite group, so a subgroup's order divides the group's order.