Answer on Abstract Algebra Question for Irvin
ϕ : U ⊗k V → K induced by u ⊗ v → uv is easily checked to be a kG-epimorphism.Since K has infinite length as a kG-module, so does W = U⊗k V . We finish by checking that W is nota semisimple kG-module. Indeed, if W is semisimple, ϕ would be a split kG-epimormorphism,so W would have a submodule with trivial G-action mappingisomorphically onto K. We have contradiction there are actually nononzero
G-fixed points in W.
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