# Answer to Question #23479 in Abstract Algebra for sanches

Question #23479

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

Expert's answer

Any

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