Math 661 Fall 2013 Homework 5 Drew Armstrong
نویسنده
چکیده
(a) Prove that [G,G]CG. (b) Prove that the quotient Gab := G/[G,G] (called the abelianization of G) is abelian. (c) If N CG is any normal subgroup such that G/N is abelian, prove that [G,G] ≤ N . (d) Put everything together to prove the universal property of abelianization: Given a homomorphism φ : G→ A to an abelian group A, there exists a unique homomorphism φ̄ := Gab → A such that φ = φ̄ ◦ π, where π : G→ Gab is the canonical surjection.
منابع مشابه
Math 661 Fall 2013 Homework 1 Solutions
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