Question #23894

Let k be any field of characteristic 3, G = S3 and let V be the kG-module ke1 ⊕ ke2 ⊕ ke3/k(e1 + e2 + e3),
on which G acts by permuting the ei’s. What is its unipotent radical?

Expert's answer

The unipotent radical of *G *isthe unique maximal normal unipotent subgroup. This unipotent radical consists

of*g **∈** G *which acttrivially on the composition factors of _{kG}V . In our case,this subgroup is clearly *<*(123)>.

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