Augmentation Quotients of Integral Group Rings

Abstract

Let G be a group, ZG the integral group ring of G and Δ(G) its augmentation ideal. M. Khambadkone [2] studies the quotient group Δ(G) Δ(H)/Δ²(G) Δ(H) when is a normal subgroup of G and gives the result that if G is the semidirect product H |>K of a finitely generated normal subgroup H by a subgroup K, then Δ(G) Δ(H)/Δ²(G) Δ(H) ≅ K|K'⊗ HIH' ⊕