20. Consider the group U9 of all units in Z9. Given that U9 is a cyclic group under multiplication, find all subgroups of U9. This is from section 3.4 of the elements of modern algebra textbook by gilbert and gilbert. In the expert solution, they find that 2 and 5 are generators, but they use only 5 to generate the subgroups of U9, why is this? Is there a reason for only using one of the generators to find the subgroups?

20. Consider the group U9 of all units in Z9. Given that U9 is a cyclic group under multiplication, find all subgroups of U9. This is from section 3.4 of the elements of modern algebra textbook by gilbert and gilbert. In the expert solution, they find that 2 and 5 are generators, but they use only 5 to generate the subgroups of U9, why is this? Is there a reason for only using one of the generators to find the subgroups?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 15E: 15. Assume that can be written as the direct sum , where is a cyclic group of order . Prove that...

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Consider the group U9 of all units in 9. Given that U9 is a cyclic group under multiplication, find all subgroups of U9.
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