Abstract
Certain subquotients of group algebras are determined as a basis for subsequent computations of relative Fox and dimension subgroups. More precisely, for a group G and N-series [Formula: see text] of G let [Formula: see text], n ≥ 0, denote the filtration of the group algebra R(G) induced by [Formula: see text], and IR(G) its augmentation ideal. For subgroups H of G, left ideals J of R(H) and right H-submodules M of [Formula: see text] the quotients IR(G)J/MJ are studied by homological methods, notably for M = IR(G)IR(H), IR(H)IR(G) + I([H, G])R(G) and [Formula: see text] for a normal subgroup N in G; in the latter case the module IR(G)J/MJ is completely determined for n = 2. The groups [Formula: see text] are studied and explicitly computed for n ≤ 3 in terms of enveloping rings of certain graded Lie rings and of torsion products of abelian groups.
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