Multiplicative Jordan Decomposition in Group Rings of 3-Groups, II

In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies the multiplicative Jordan decomposition (MJD). In the nonabelian case, we show that ℤ[G] sa...

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Bibliographic Details
Published in:Communications in algebra 2014-06, Vol.42 (6), p.2633-2639
Main Authors: Liu, Chia-Hsin, Passman, D. S.
Format: Article
Language:English
Subjects:
3-group
Algebra
Classification
Decomposition
Integral group ring
Integrals
Mathematical analysis
Multiplicative Jordan decomposition
Rings (mathematics)
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Summary:In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies the multiplicative Jordan decomposition (MJD). In the nonabelian case, we show that ℤ[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 3 3  = 27.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2013.766828