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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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?
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