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1) and 3 = 2 subgroup of S₁ generated by a and B. G acts on the set X = {1,2,3,4} x {1,2,3,4}: if o G, then a(i, j)= (o(i), o(j)). a. For x = (1, 1), y = (1,3), and z= (1,4) in X, 12. Let a = 2 3 1 2 3 4 2 3 4 1 3), and let G = {e, a, a², a³, B,aß‚a²ß,a³ß} be the 1 4 3 find the orbits Oz, Oy, 029 and the stabilizers Gr, Gy, Gz. b. Find the partition of X given by the orbits of G. c. For elements g = a²ß and h = a³ß of G, find the fixed sets X, and X₁.

1) and 3 = 2 subgroup of S₁ generated by a and B. G acts on the set X = {1,2,3,4} x {1,2,3,4}: if o G, then a(i, j)= (o(i), o(j)). a. For x = (1, 1), y = (1,3), and z= (1,4) in X, 12. Let a = 2 3 1 2 3 4 2 3 4 1 3), and let G = {e, a, a², a³, B,aß‚a²ß,a³ß} be the 1 4 3 find the orbits Oz, Oy, 029 and the stabilizers Gr, Gy, Gz. b. Find the partition of X given by the orbits of G. c. For elements g = a²ß and h = a³ß of G, find the fixed sets X, and X₁.

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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12. Let a = 1) and 3 = 23 2 3 4 1 1 2 3 4 3), and let G = {e, a, a², a³, B,aß‚a²ß,a³ß} be the 1 4 3 2 subgroup of S₁ generated by a and B. G acts on the set X = {1,2,3,4} x {1,2,3,4}: if o G, then a(i, j)= (o(i), o(j)). a. For x = (1, 1), y = (1, 3), and z = (1,4) in X, find the orbits Oz, Oy, 029 and the stabilizers Gr, Gy, Gz. b. Find the partition of X given by the orbits of G. c. For elements g = a²ß and h = a³ß of G, find the fixed sets X, and X₁.
Transcribed Image Text:12. Let a = 1) and 3 = 23 2 3 4 1 1 2 3 4 3), and let G = {e, a, a², a³, B,aß‚a²ß,a³ß} be the 1 4 3 2 subgroup of S₁ generated by a and B. G acts on the set X = {1,2,3,4} x {1,2,3,4}: if o G, then a(i, j)= (o(i), o(j)). a. For x = (1, 1), y = (1, 3), and z = (1,4) in X, find the orbits Oz, Oy, 029 and the stabilizers Gr, Gy, Gz. b. Find the partition of X given by the orbits of G. c. For elements g = a²ß and h = a³ß of G, find the fixed sets X, and X₁.
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