Question 2: a. Let G be a group and a E G. Show that if |a| = n, then |a¹| = n. b. Without computing the orders, explain why the two elements 7 and 13 from U(15) must have the same order. (Hint: Use the result of question 2 - part a).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let G be a group
Question 2:
a. Let G be a group and a E G. Show that if |a| = n, then
|a¹| = n.
b. Without computing the orders, explain why the two
elements 7 and 13 from U(15) must have the same
order. (Hint: Use the result of question 2 - part a).
Question 3:
Transcribed Image Text:Question 2: a. Let G be a group and a E G. Show that if |a| = n, then |a¹| = n. b. Without computing the orders, explain why the two elements 7 and 13 from U(15) must have the same order. (Hint: Use the result of question 2 - part a). Question 3:
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