Question

30. A partial operation table for a group G = {e, a, b, c, d,f} is shown below. Complete the table. (Hint: Exercises 27 and 28.] e a b c e a b c a a be a d d f f

Answer 1

e Te a a b c b c at. dit a fed and column (A) we know by the one per row role tant ad af and of c. leased to Ta & e d te 2 р (4) we know tant coaf. so do (acha aleg of ce de=cacha - acca) afac

ele a 6 c at a dtc a. + (c cf=a , this af = (ac)t = acf = a = b. (6) donc so bd = d(aa) daa= canto (2) 4:6, it = adf af safe. & we know sant . so base a. (8) deat, so f6 = (ad) = adb eaf = c. trick, (1) touc, e6=(af) & a off anced. (il grein by the one per row and column 6 6 a beaf and fd = c. o ela, so cc = cff 6) = off cas-e. (k) we see that dob, desa, ddae, te=p and fd=a.

e a e a car c d t b d fc 61 e a fed е 4 а a d c t a e f. tt dc & a e.