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 $$
\qquad k \otimes_{\mathbb {Z}} {R}_{\mathbb{Q}} = \overline{I_{1}} \supseteq \overline{I_{2}}
\supseteq \overline{I_{3}} \supseteq \raisebox{0.5ex}{\ldots}$$
@article{1148059340,
author = {Bourizk, Isma\"\i l},
title = {A remark on a functor of rational representations},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {12},
number = {5},
year = {2006},
pages = { 149-157},
language = {en},
url = {http://dml.mathdoc.fr/item/1148059340}
}
Bourizk, Ismaïl. A remark on a functor of rational representations. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp. 149-157. http://gdmltest.u-ga.fr/item/1148059340/