Question

Asked Oct 25, 2019

Step 1

The group **G = (Z/18Z, +)** be a cyclic group of order **18** so, the group **G** is similar to Z_{18}.

Part (a):

A subgroup H of the group **G** such that **|H|=3**. Here 18 is divided by 3.

So, the subgroup of order 3 in a cyclic group of order **18 (Z _{18})** is only one group which is

And similarly H can be written as:

Step 2

Part (b):

The elements of G/H:

Step 3

Z/H = {(0,6,12),(1,7,13),(2,8,14),(3,9,15),(4,10,16),(5,11,17)}

H={0,6,12}

H+1 = {1,7,13}

H+2 ={2,8,14}

&n...

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