In Z16, write down all the cosets of the subgroup H = {[0], [4], [8], [12]).(Since the operation in Z, is +, write your coset as [a] + H. We don'tneed to distinguish between right cosets and left cosets, since Z, isabelian under +.)

We see, elements of Z16 are {[0], [1], [2], [3], [4], [5], [6], . . . . . . . , [15]} H = {[0], [4],…

Answered: In Z₁6, write down all the cosets of…

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 7E: Write 20 as the direct sum of two of its nontrivial subgroups.

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In Z₁6, write down all the cosets of the subgroup H = {[0], [4], [8], [12]}. (Since the operation in Z, is +, write your coset as [a] + H. We don't need to distinguish between right cosets and left cosets, since Z₁ is abelian under +.)