Definition of Normal Subgroups | Abstract Algebra

Support the production of this course by joining Wrath of Math to access all my Abstract Algebra videos plus lecture notes at the premium tier!    / @wrathofmath   🛍 Check out the coolest math clothes in the world: https://mathshion.com/ Abstract Algebra course:    • Abstract Algebra   Abstract Algebra exercises:    • Abstract Algebra Exercises   Get the textbook! https://amzn.to/45IvVgH Business Inquiries: wrathofmathlessons@gmail.com 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 Subgroup ...   ★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 Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu