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Question 6 Let G be a group, and a € G. Define the function fa: G→G by f(x) = ax. (i) Show that fa is a bijection. (One way to do this is to find the inverse function.) (ii) Suppose we made the group operation table for G (as we did a few times in lecture for various groups). What does part (i) tell us about the rows of this table?

Question 6 Let G be a group, and a € G. Define the function fa: G→G by f(x) = ax. (i) Show that fa is a bijection. (One way to do this is to find the inverse function.) (ii) Suppose we made the group operation table for G (as we did a few times in lecture for various groups). What does part (i) tell us about the rows of this table?

Advanced Engineering Mathematics
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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Question 6 Let G be a group, and a € G. Define the function fa: G→ G by f(x) = = ax. (i) Show that fa is a bijection. (One way to do this is to find the inverse function.) (ii) Suppose we made the group operation table for G (as we did a few times in lecture for various groups). What does part (i) tell us about the rows of this table?
Transcribed Image Text:Question 6 Let G be a group, and a € G. Define the function fa: G→ G by f(x) = = ax. (i) Show that fa is a bijection. (One way to do this is to find the inverse function.) (ii) Suppose we made the group operation table for G (as we did a few times in lecture for various groups). What does part (i) tell us about the rows of this table?
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