Exercise 10, § 2

Let G be a group and H a normal subgroup of G. Show that, if $a$ is the two-sided ideal of the group algebra $A^{(G)}$, generated by the elements $ts - s$, where $t$ runs through H and $s$ runs through G, the group algebra $A^{(G/H)}$ is isomorphic to the quotient algebra $A^{(G)}/a$.