MT1sol - Math 113 Solutions to Midterm Exam 1(1 This is part(ii of Problem 30 on page 45 By the Binomial Theorem p(a b)p = i=0 p ai bpi i where p i =

MT1sol - Math 113 Solutions to Midterm Exam 1(1 This is...

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Math 113, Solutions to Midterm Exam # 1 (3) LetGbe an abelian group andHany subgroup.ForgGandhHwe haveg-1h=hg-1and henceg-1hg= (g-1h)g= (hg-1)g=h(g-1g) =hH.This shows thatHis a normal subgroup ofG.(4)

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