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How many elements of order 9 does Z3 Z9 have (Do not do

Chapter 8, Problem 10E

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QUESTION:

Problem 10E

How many elements of order 9 does Z3 ⊕ Z9 have? (Do not do this exercise by brute force.)

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QUESTION:

Problem 10E

How many elements of order 9 does Z3 ⊕ Z9 have? (Do not do this exercise by brute force.)

ANSWER:

Step 1 of 3

The order of an element in a direct product of a finite number of finite groups is the least common multiple of the orders of the components of the element. In symbols,

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