Author: 
Serge Bouc, UFR de Mathematiques, Universite Paris 7-Denis Diderot, 2 Place Jussieu, 75251 Paris Cedex 05, France.
Abstract:
A well-known theorem proved independently by Ritter and Segal states that if $P$ is a $p$-group, then the natural morphism from the Burnside ring $B(P)$ of $P$ to the Grothendieck ring $R_{\Q}(P)$ of rational representations of $P$, mapping a finite $P$-set $X$ to the permutation module $\Q X$, is surjective.
The object of this note is to give a more explicit version of this theorem: for every non-trivial irreducible $\Q P$-module $V$ there is a short exact sequence
$$0\to V\to \Q P/Q \to \Q P/R \to 0$$
where $Q$ and $R$ are subgroups of $P$ with $|R:Q|=p$.