Prerna chaudhary 1 Asked a Question
October 16, 2021 1:12 ampts 30 pts
Let G be a group and let G' be the subgroup of G generated by the set S {x'yr'y | x, y E G}. (See Exercise 3, Supplementary Exercises for Chapters 5-8, for a more complete description of G'.) a. Prove that G is normal in G b. Prove that G/G is Abelian. C. If G/N is Abelian, prove that G' N. d. Prove that if H is a spbgroup ofG and GSH, then H is normal in G.
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