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In Group Theory from Abstract Algebra, if we are given a group G and a subgroup H of G, we say that H is a normal subgroup of G, written H ⊲ G, if aH = Ha for all a in G. That is, if, for all elements "a" of the group G, the left coset of H in G containing "a" equals the right coset of H in G containing "a". There is also a normal subgroup test. All the conjugate subgroups of H in G need equal H itself. In other words, H is the unique conjugate subgroup to itself. 🔴 "Contemporary Abstract Algebra", by Joe Gallian: https://amzn.to/2ZqLc1J 🔴 Abstract Algebra Exam 1 Review Problems and Solutions: • Abstract Algebra Exam 1 Review Problems an... 🔴 Abstract Algebra Exam 2 Review Problems and Solutions: • Abstract Algebra Exam 2 Review Problems an... 🔴 Abstract Algebra Exam 3 Review Problems and Solutions: • Abstract Algebra Exam 3 Review Problems an... 🔴 Abstract Algebra Final Exam Review Problems and Solutions: • Abstract Algebra Final Exam Review Problem... 🔴 Abstract Algebra Problems with Solutions (including Proofs): • Abstract Algebra Problems with Solutions (... 🔴 Abstract Algebra Lectures Playlist: • Abstract Algebra Course, Lecture 1: Introd... 🔴 Check out my blog at: https://infinityisreallybig.com/ #AbstractAlgebra #GroupTheory #NormalSubgroup Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: / billkinneymath 🔴 Follow me on Instagram: / billkinneymath 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.