Abstract
An important result of Ritter (1972) and Segal (1972) states that if P is a p-group, then the natural morphism s from the Burnside ring B(P) of P to the Grothendieck ring R ℚ(P) of rational representations of P: is surjective, where R is a subgroup of P. The purpose of this note is to show that if k is a field of positive characteristic p, then for a finite p-group P, the k-vector space k⊗ℤ R ℚ(P) is generated by , for subgroups R of P having index lower than p in their normalizer, and , for subgroups Z ⊃ R of P whenever N P (R)/R is cyclic or quaternion, and Z/R is its unique subgroup of order p.
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