The augmentation quotients of the groups of order \(2^5\). II. (English) Zbl 1206.16017
Let \(G\) be a finite group, \(\mathbb{Z} G\) its integral group ring, \(\Delta\) the augmentation ideal. The additive subgroups of the factors \(\Delta^n/\Delta^{n+1}\) were the subject of intensive research mainly in the Abelian case, but the problem for nonabelian groups was also considered in certain cases.
In the first part of this paper [Commun. Algebra 37, No. 9, 2956-2977 (2009; Zbl 1182.16019)], the authors determined a \(\mathbb{Z}\)-basis for powers of the augmentation ideal for 35 of the 44 nonabelian groups of order 32, the remaining 9 groups and an Abelian group of order 32 not treated yet in the literature are the subject matter of the present article.
In the first part of this paper [Commun. Algebra 37, No. 9, 2956-2977 (2009; Zbl 1182.16019)], the authors determined a \(\mathbb{Z}\)-basis for powers of the augmentation ideal for 35 of the 44 nonabelian groups of order 32, the remaining 9 groups and an Abelian group of order 32 not treated yet in the literature are the subject matter of the present article.
Reviewer: János Kurdics (Nyíregyháza)
MSC:
| 16S34 | Group rings |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
Citations:
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