Some Intersection Theorems and Subgroups Determined by Certain Ideals in Integral Group Rings, Ⅱ

• 来源期刊: 代数集刊（英文版）
• 关键词: integral group ring augmentation ideal subgroups determined by ideals
• 年，卷（期）: 2002,（2）
• 页码范围: 135-142
• 页数: 8页
• 语种: 英文

摘要

Let ZG be the integral group ring of a group G, and I(G) its augmentation ideal. For a free group F and a subgroup Rof F, the intersections I3(F) ∩ I2(R) and I3(F) ∩ I(R) are determined. For an arbitrary group G and a subgroup H of G, the subgroup G ∩ (1 + I2(G)I(H)) is identified when either H/H′ or G/HG′ is torsion-free. Also, when S is another subgroup of F and R is normal in F, the subgroup F ∩ (1 + ZFI2(R)I(S)) of F is identified.