Gbe a finite group and letNbe a normal subgroup ofG.Suppose that the ordernofNis relatively prime to the index|G:N|=m.(a)Prove thatN={a∈G∣an=e}(b)Prove thatN={bm∣b∈ Q5. G be a finite group and let N be a normal subgroup of G.Suppose that the order n of N is relatively prime to the index G:N=m.(a) Prove that N={a€G|a"=e}(b) Prove that N={b"|b€G}

Given G is a finite group and N is a normal subgroup of G. The order n of N is relatively prime to…

Answered: Q5. G be a finite group and let N be a…

Q5. G be a finite group and let N be a normal subgroup of G. Suppose that the order n of N is relatively prime to the index |G:N=m. (a) Prove that N={a€G|a"=e} (b) Prove that N={b"|bEG}

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 21E

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Gbe a finite group and letNbe a normal subgroup ofG.Suppose that the ordernofNis relatively prime to the index|G:N|=m.(a)Prove thatN={a∈G∣an=e}(b)Prove thatN={bm∣b∈

Q5. G be a finite group and let N be a normal subgroup of G.
Suppose that the order n of N is relatively prime to the index G:N=m.
(a) Prove that N={a€G|a"=e}
(b) Prove that N={b"|b€G}

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