1. (10 pts) Let X = f1; 2; 3; 4; s1; s2; s3; s4; m1; m2; d1; d2; C; P1; P2; P3; P4g be the D4-set of Example 16:8 with the action table in Table 16:10 (see pages 156; 157). Let G = D4 = 1; r; r2; r3; s; sr; sr2; sr3: Find the following.a) Find each xed set Xg; g 2 G: b) Find the isotropy groups Gx; x 2 X: c) The orbits Ox; x 2 G 2. (10pts) Consider O(2) = SO(2)[SO(2); where SO(2) =cos sin sin cos2 O(2) j 2 [0;2), =1 0 0 1. Denote by r =cos sin sin cos2 SO(2); 2 [0;2): Dene : O(2)R2 !R2; as follo...
Get Answer
