Manfred Hartl. 
Une approche homologique des quotients et sous-groupes de Fox. 

Abstract : Let $G$ be a group, $H$ a subgroup of $G$ and $I(G)$ the 
augmentation ideal of the group ring $\Z(G)$. If
$H$ is free or is a semidirect factor of $G$, then the Fox quotients 
$Q_n(G,H)= I^{n-1}(G)I(H)/I^n(G)I(H)$ are computed for all
$n>1$, in the latter case in terms of certain tensor products of 
filtration quotients of $H$ and of the complementary subgroup. A link
between the Fox subgroups $F_n(G,H) = G \cap (1 + I^n(G)I(H))$ and 
the homology of $H$ is etablished and exploited in the case
that $H$ is free. Moreover, an adaptation to Fox quotients of 
Quillen's appoximation of the associated graded of the group ring is
introduced and studied in low dimensions.