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Chapter 7: 56E (page 213)

Show that the group U₂₀ of the units in Z₂₀is not cyclic.

Short Answer

Expert verified

It has been proved that U₂₀is not cyclic.

Step by step solution

Observe elements of U20

Since, $U_{20} = {1, 3, 7, 9, 11, 13, 17, 19}$ .

Subgroups generated by 9, 11, 19 are of order 2.

Conclusion

Here, U₂₀has more than 1 subgroup of order 2. Therefore, the group is not cyclic.

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Show that the group U₂₀ of the units in Z₂₀is not cyclic.

Short Answer

Step by step solution

Observe elements of U20

Conclusion

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Show that the group U20 of the units in Z20is not cyclic.

Short Answer

Step by step solution

Observe elements of U20

Conclusion

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Show that the group U₂₀ of the units in Z₂₀is not cyclic.