Multiplicative jordan decomposition in group rings of 2, 3-groups

Chia Hsin Liu, D. S. Passman, T. Y. Lam

研究成果: 雜誌貢獻期刊論文同行評審

8 引文 斯高帕斯(Scopus)

摘要

In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that ℤ[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, while the corresponding 3-groups were almost completely determined by the present authors. Thus, we are concerned here, for the most part, with groups whose order is divisible by 6. As it turns out, there are precisely three nonabelian 2, 3-groups, of order divisible by 6, with ℤ[G] satisfying MJD. These have orders 6, 12, and 24. In view of another result of Hales, Passi and Wilson, this completes a significant portion of the classification of all finite groups with MJD.

原文英語
頁(從 - 到)483-492
頁數10
期刊Journal of Algebra and its Applications
9
發行號3
DOIs
出版狀態已發佈 - 2010 六月

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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