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Answer to Question #18104 in Abstract Algebra for sanches

Question #18104
Assume char k = 2. Let A be an abelian 2'-group and let G be the semidirect product of A and a cyclic group <x> of order 2, where x acts on A by a → a^−1. If |A| < ∞, show that rad kG = k (Sum over g∈G)•g, and (rad kG)^2 = 0.
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