Normal subgroups are a powerful tool for creating factor groups (also called quotient groups). In this video we introduce the concept of a coset, talk about which subgroups are “normal” subgroups, and show when the collection of cosets can be treated as a group of their own. As a motivation, we will begin by discussing congruences. Our Abstract Algebra playlist is here: Be sure to subscribe so you don't miss new lessons from Socratica: ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : ► Make a one-time PayPal donation: ► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank you! ♦♦♦♦♦♦♦♦♦♦ We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition Milne, Algebra Course Notes (available free online) ♦♦♦♦♦♦♦♦♦♦ Connect with us! Facebook: Instagram: Twitter: ♦♦♦♦♦♦♦♦♦♦ Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison ♦♦♦♦♦♦♦♦♦♦