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6.9. Let G = Cn be a cyclic group of order n, and let X = {x₁,...,n} be a set containing n elements. For each part, find an action of G on X so that there is an element x = X having the indicated property. (a) The stabilizer is Gx = {e}. (b) The stabilizer is Gx (c) The orbit is Gx = {x}. (d) The orbit is Gx = X. = G. -

6.9. Let G = Cn be a cyclic group of order n, and let X = {x₁,...,n} be a set containing n elements. For each part, find an action of G on X so that there is an element x = X having the indicated property. (a) The stabilizer is Gx = {e}. (b) The stabilizer is Gx (c) The orbit is Gx = {x}. (d) The orbit is Gx = X. = G. -

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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**6.9.** Let \( G = C_n \) be a cyclic group of order \( n \), and let \( X = \{ x_1, \ldots, x_n \} \) be a set containing \( n \) elements. For each part, find an action of \( G \) on \( X \) so that there is an element \( x \in X \) having the indicated property. (a) The stabilizer is \( G_x = \{ e \} \). (b) The stabilizer is \( G_x = G \). (c) The orbit is \( Gx = \{ x \} \). (d) The orbit is \( Gx = X \).
Transcribed Image Text:**6.9.** Let \( G = C_n \) be a cyclic group of order \( n \), and let \( X = \{ x_1, \ldots, x_n \} \) be a set containing \( n \) elements. For each part, find an action of \( G \) on \( X \) so that there is an element \( x \in X \) having the indicated property. (a) The stabilizer is \( G_x = \{ e \} \). (b) The stabilizer is \( G_x = G \). (c) The orbit is \( Gx = \{ x \} \). (d) The orbit is \( Gx = X \).
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