Group Homomorphisms in Abstract Algebra

A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be used through abstract algebra. You will study homomorphisms between groups, rings, fields, modules, vector spaces, and more. Correction note: at 6:10 -i in the second table should be outlined in purple. Thank you to viewer Power Max for catching this! ♦♦♦♦♦♦♦♦♦♦ This video was made possible by our VIP Patrons on Patreon! Thank you for supporting our work this year. Because of you, we are able to continue making the highest quality math videos, free for the world. We would like to thank Tracy Karin Prell, Carlos Araujo, Markie Waid, Martin Stephens, David Borger, Burhan Saifaddin, MdeG, Michael, Umar Khan, John Krawiec, Patrick Cool, Tim Tapio, Deeptanshu Malik, Kevin B, Terrill Frantz, and Charles Southerland, and our newest VIP Patron, Andre Gibbs. 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! ♦♦♦♦♦♦♦♦♦♦ 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 ♦♦♦♦♦♦♦♦♦♦ 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 ♦♦♦♦♦♦♦♦♦♦