Question
Asked Sep 17, 2019

32

e for all a in G. (Note that n is indep
tnat a
32. Determine the subgroup lattice for Z
33. Determine the subgroup lattice for Za where p an
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e for all a in G. (Note that n is indep tnat a 32. Determine the subgroup lattice for Z 33. Determine the subgroup lattice for Za where p an

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Expert Answer

Step 1

To ddscribe the lattice structure of the set of all subgroups of the group Z12

Step 2

This group is cyclic of order 12, for example, generated by 1, (recall 1 has order 12 in this group)

Now,Z =0,1,2..1,is a cyelic
group.nder addition modulo 12.
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Now,Z =0,1,2..1,is a cyelic group.nder addition modulo 12.

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Step 3

As the group is cyclic of order 12, every subgroup is al...

The 6 subgroups of Zy
03,<6= {0,6,<4>= {0,4,8}|
<3>= {0,3,6,9},<2>= {0,2,4,6,8,10,12},
<l>=Z12
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The 6 subgroups of Zy 03,<6= {0,6,<4>= {0,4,8}| <3>= {0,3,6,9},<2>= {0,2,4,6,8,10,12}, <l>=Z12

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