Augmentation Quotients of Free Group Rings

摘要

Let F be a free group and R be a subgroup of F. It is proved that△n(F)△m(R)/△n+1(F)△m(R),△n(F)△m (R)/△n-1(F)△m+1 (R),△n(F)△m(R)/△n(F)△m+1(R)are free-abelian. Explicit bases of first two and. complete descriptions of all these groups are also given.