Cosets and Lagrange’s Theorem - The Size of Subgroups (Abstract Algebra)

Lagrange’s Theorem places a strong restriction on the size of subgroups. By using a device called “cosets,” we will prove Lagrange’s Theorem and give some examples of its power. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation: https://www.paypal.me/socratica ► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank you! ♦♦♦♦♦♦♦♦♦♦ Connect with us! Facebook: https://www.facebook.com/SocraticaStudios/ Instagram: https://www.instagram.com/SocraticaStudios/ Twitter: https://twitter.com/Socratica ♦♦♦♦♦♦♦♦♦♦ Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison ♦♦♦♦♦♦♦♦♦♦