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Let D3 be the dihedral group for the equilateral triangle ABC. Let r be counterclockwise rotation by (27/3), and let s be the flip that leaves A fixed and exchanges B and C. a) Write down the Cayley table for D3 in terms of r and s. b) Let G = Z3 x Z2, where Zn is defined in Problem 1 above. Define the following notation: r = (1,0) and s = (0,1). Write the Cayley table for G in terms of r and s. c) Is G is isomorphic to D3? Explain your answer

Let D3 be the dihedral group for the equilateral triangle ABC. Let r be counterclockwise rotation by (27/3), and let s be the flip that leaves A fixed and exchanges B and C. a) Write down the Cayley table for D3 in terms of r and s. b) Let G = Z3 x Z2, where Zn is defined in Problem 1 above. Define the following notation: r = (1,0) and s = (0,1). Write the Cayley table for G in terms of r and s. c) Is G is isomorphic to D3? Explain your answer

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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Let D3 be the dihedral group for the equilateral triangle ABC. Let r be counterclockwise rotation by (27/3), and let s be the flip that leaves A fixed and exchanges B and C. a) Write down the Cayley table for D3 in terms of r and s. b) Let G = Z3 x Z2, where Zn is defined in Problem 1 above. Define the following notation: r = (1,0) and s = (0,1). Write the Cayley table for G in terms of r and s. c) Is G is isomorphic to D3? Explain your answer
Transcribed Image Text:Let D3 be the dihedral group for the equilateral triangle ABC. Let r be counterclockwise rotation by (27/3), and let s be the flip that leaves A fixed and exchanges B and C. a) Write down the Cayley table for D3 in terms of r and s. b) Let G = Z3 x Z2, where Zn is defined in Problem 1 above. Define the following notation: r = (1,0) and s = (0,1). Write the Cayley table for G in terms of r and s. c) Is G is isomorphic to D3? Explain your answer
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