ABSTRACT ALGEBRAIC

U (Z 82) G s d D | l x ] x 3 d + x) = Had 1 7 xex Use the table to the left to find the following adoes 49 x2 2x W N a. 15 x3 3x Find the elements of G/(xe4x). (10 pts) 23 x4 0 4x 5 79 e 5x 6 61 x e 6x (lining 2) $215200 smee or H + 5x bris H + 548 OTA 7 17 x2 2 7x 8 37 x 3 9 13 xtex 0 b. Create the Cayley table for G/(xe*x). (May be extra spaces) (10 pts) 9 e 2x 11 63 x e3x .8 12 31 x2 e 4x 13 53 x3 e 5x 14 43 x4 e 6x 15 55 e 7x 16 57 x 17 71 x2ex 18 5 x3 e 2x 19 35 x 4 2 3x 20 81 e 4x 21 75 * esx ads 22 33 x2 e 6x 23 67 x3 e 7x SO6 24 59 1 4 25 3 ex 26 21 x e 2 x 5 points) c. Without having the Cayley table, we know G/(xe*x) is cyclic. Why? fad 27 65 x2e 3x 28 45 x3 e 4x 29 69 xte 5x H 10 arseoo fal bria 30 73 e 6x 31 19 Xe7x 32 51 x2 33 29 xsex 34 39 x4 @ 2x .H lo alozoo fight bail 35 27 e 32 36 25 x e 4x 37 11 x2 5x 38 77 x3 6x 39 47 x 4 07x D C H al 0 1 1