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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 48E
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