Question 8.(a) In the group → Z10, >, find ([2]) and then find the order of the quotient group Z₁0/([2]).(b) Prove or disprove: Z10 ~ Z5 x Z₂-(c) Prove that G/N is Abelian iff aba-¹6-¹ N Va,b € G.(d) Find the cosets of the quotient group (5)/(10), and determine its order.

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Question 8. (a) In the group < Z10,>, find ([2]) and then find the order of the quotient group Z₁0/([2]).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 21E

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