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Calculate the number of elements of order 2 in each of

Chapter 11, Problem 4E

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QUESTION:

Calculate the number of elements of order 2 in each of \(Z_{16}, Z_8 \oplus Z_2, Z_4 \oplus Z_4\), and \(Z_4 \oplus Z_2 \oplus Z_2\). Do the same for the elements of order 4.

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QUESTION:

Calculate the number of elements of order 2 in each of \(Z_{16}, Z_8 \oplus Z_2, Z_4 \oplus Z_4\), and \(Z_4 \oplus Z_2 \oplus Z_2\). Do the same for the elements of order 4.

ANSWER:

Step 1 of 4

From cyclic group by the theorem 4.4 it is element of order.

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