Answer to Question #18648 in Abstract Algebra for Hym@n B@ss

Question #18648

For G = S3 and any field k of characteristic 2, view V = ke1 ⊕ ke2 ⊕ ke3/k(e1 + e2 + e3) as a (simple) kG-module with the permutation action. Show that W = V ⊗k V with the diagonal G-action is not a semisimple kG-module.

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