Uploaded December 2020 | Updated September 2026, 1 week ago

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Proof that cosets are disjoint: youtu.be/uxhAUmgSHnI

In order for a subgroup to create a quotient group (also known as factor group), it must be a normal subgroup. That means that when we conjugate an element in the subgroup, it stays in the subgroup. In this video, we explain why conjugation is so important to quotient groups!

Group Theory playlist: youtube.com/playlist?list=PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ6a6

0:00 Intro to quotient groups
5:10 Not all subgroups work!
8:28 Quotient group condition
12:15 Normal subgroup examples

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Music: OcularNebula - The Lopez