A remark on a functor of rational representations

Abstract

Let $k$ be a field of positive characteristic $p$. First we describe some specific subfunctors of the Burnside functor $ k \otimes_{\mathbb {Z}} B $. We prove next that the restriction of the functor of rational representations $ k \otimes_{\mathbb {Z}} {R}_{\mathbb{Q}} $ to abelian finite $p$-groups, has a unique maximal filtration $$ \qquad k \otimes_{\mathbb {Z}} {R}_{\mathbb{Q}} = \overline{I_{1}} \supseteq \overline{I_{2}} \supseteq \overline{I_{3}} \supseteq \raisebox{0.5ex}{\ldots}$$