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Without actually computing the orders, explain why the two
Chapter 3, Problem 5E(choose chapter or problem)
Without actually computing the orders, explain why the two elements in each of the following pairs of elements from Z30 must have the same order: {2, 28}, {8, 22}. Do the same for the following pairs of elements from U(15): {2, 8}, {7, 13}.
Questions & Answers
QUESTION:
Without actually computing the orders, explain why the two elements in each of the following pairs of elements from Z30 must have the same order: {2, 28}, {8, 22}. Do the same for the following pairs of elements from U(15): {2, 8}, {7, 13}.
ANSWER:Step 1 of 3
Order of an Element: The order of an element in any given group, say can be defined by any positive integer with the smallest value. In case it does not have such integer value, the element is said to have infinite order.