3. The dihedral group of degree 4, D4 {1,r,r², r³, s, sr, sr², sr³}, is the group of symmetries of a square, where r den

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3 The Dihedral Group Of Degree 4 D4 1 R R R S Sr Sr Sr Is The Group Of Symmetries Of A Square Where R Den 1 (178.53 KiB) Viewed 47 times

3. The dihedral group of degree 4, D4 {1,r,r², r³, s, sr, sr², sr³}, is the group of symmetries of a square, where r denotes a 90° rotation clockwise and s denotes a reflection about a vertical axis. By labeling the vertices of a square, we can think of elements of D4 as permutations of the set {1, 2, 3, 4]. = (a) Write r and s as permutations of the set {1,2,3,4}. (b) Using the way you've written r and s in part (a), show that rs = sr³.