Question

Let H be a normal subgroup of G. Show that I = kG • rad kH is an ideal of kG.

Answer 1

Any σ ∈ G defines a conjugation automorphism on thesubring kH ⊆ kG, and this automorphism must takeradkH to rad kH. Therefore, (rad kH)σ ⊆ σ · rad kH ⊆ I, which shows that I is anideal of kG.