Let K={k1,....km} be a conjugacy class in the finite group G.

a) Prove that the element K=k1+k2+....km is the center of the group ring R[G]

(check that g^-1Kg=K for all gin G)

b) Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki. Prove that an element alpha of R[G] is in the center of R[G] iff alpha=a1K1 +.....+arKr for some a1,...ar in R