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Definition of Normal Subgroups | Abstract Algebra

We introduce normal subgroups with their conjugate definition and the coset definition. We'll see examples of normal subgroups and nonexamples of normal subgroups, and we finish with a proof that every subgroup of an abelian group is a normal subgroup. A subgroup H of a group G is normal if H is closed with respect to conjugates, or equivalently if each left coset aH is equal to each right coset Ha for every a in G. #abstractalgebra #grouptheory Proving Equivalent Definitions of Normal Subgroups:    • Equivalent Definitions of Normal Subg...   Abstract Algebra Course:    • Abstract Algebra   Abstract Algebra Exercises:    • Abstract Algebra Exercises   ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Abstract Algebra: https://amzn.to/3IjoZaO Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020