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Coset Multiplication on Normal Subgroups | Abstract Algebra

We give the definition of coset multiplication. We find that it is not well-defined however, because products of equal cosets may give different results. We see an example of this failure in the symmetric group of permutations S3. We then prove that coset multiplication is well defined on the set of all cosets of a normal subgroup. #abstractalgebra #grouptheory Normal Subgroups:    • Definition of Normal Subgroups | Abst...   Left and Right Cosets in 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 Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER 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 Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, and Shadow Master for their generous support on Patreon! Outro music is mine. You cannot find it anywhere, for now. Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Math Rap channel:    / @mathbars2020