Abstract The augmentation powers in an integral group ring ℤ ⁢ G {\mathbb{Z}G} induce a natural filtration of the unit group of ℤ ⁢ G {\mathbb{Z}G} analogous to the filtration of the group G given by its dimension series { D n ⁢ ( G ) } n ≥ 1 {\{D_{n}(G)\}_{n\geq 1}} . The purpose of the present article is to investigate this filtration, in particular, the triviality of its intersection.

中文翻译：

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积分群环中的单位和增强能力

摘要 积分群环 ℤ ⁢ G {\mathbb{Z}G} 中的增广幂引起 ℤ ⁢ G {\mathbb{Z}G} 的单位群的自然过滤，类似于由下式给出的群 G 的过滤其维数级数 { D n ⁢ ( G ) } n ≥ 1 {\{D_{n}(G)\}_{n\geq 1}} 。本文的目的是研究这种过滤，特别是其交集的琐碎性。