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Answer to Question #23714 in Abstract Algebra for jeremy

Question #23714
For any field k and for any normal subgroup H of a group G, assume further that [G : H] is finite and prime to char k. Let V be a kG-module and W be a kH-module. Show that V is a semisimple kG-module iff kHV is a semisimple kH-module.
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