MULTIPLICATIVE JORDAN DECOMPOSITION IN GROUP RINGS OF 3-GROUPS

被引：9

作者：

Liu, Chia-Hsin ^{[1
]}

Passman, D. S. ^{[2
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, Taipei, Taiwan

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2009年 / 8卷 / 04期

关键词：

Integral group ring; multiplicative Jordan decomposition; 3-group;

D O I：

10.1142/S0219498809003461

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we essentially classify those finite 3-groups G having integral group rings with the multiplicative Jordan decomposition property. If G is abelian, then it is clear that Z[G] satisfies MJD. Thus, we are only concerned with the nonabelian case. Here we show that Z[G] has the MJD property for the two nonabelian groups of order 3(3). Furthermore, we show that there are at most three other specific nonabelian groups, all of order 34, with Z[G] having the MJD property. Unfortunately, we are unable to decide which, if any, of these three satisfies the appropriate condition.

引用

页码：505 / 519

页数：15