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-¹b-¹ N Va, b € G.(d) Find the cosets of the quotient group (5)/(10), and determine its order.

(a). The given group is ℤ10,⊕, the additive group of integer modulo 10. We know that the group 2 is…

Answered: In the group < Z10, >, find ([2]) and…

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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In the group < Z10, >, find ([2]) and then find the order of the quotient group Z10/([2]). Prove or disprove: Z10 Z5 x Z₂. Prove that G/N is Abelian iff aba-¹b-¹ N a, b E G. Find the cosets of the quotient group (5)/(10), and determine its order.