La suspension homologue pour les CW-complexes quotients d'actions libres de $((Z\mathrm{/}2{)}^n$

This note shows that the $n$-th homology suspension is surjective for certain quotients of finite $((Z\mathrm{/}2{)}^n$-CW.complexes. This is true as soon as the equivariant $((Z\mathrm{/}2{)}^n$-cohomology are quotients is a free $H^{\ast }$((Z/2)^n$-module. An application is given to certain Brown-Gitler spectrum.