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首页> 外文期刊>Journal of algebra and its applications >Multiplicative jordan decomposition in group rings of 2, 3-groups
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Multiplicative jordan decomposition in group rings of 2, 3-groups

机译：2组，3组的环中的可乘约旦分解

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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 ?[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 ?[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.
机译：在本文中，我们基本上完成了具有整数组环且具有可乘约旦分解（MJD）性质的有限2、3组G的分类。如果G是阿贝尔群或哈密顿2群，则显然[[G]满足MJD。因此，我们只需要考虑非阿贝尔情况。回想一下，具有MJD的2组完全由Hales，Passi和Wilson决定，而相应的3组几乎由本作者完全确定。因此，在这里，我们主要关心的是其阶数可被6整除的组。事实证明，恰好存在三个可被6整除的阶的非阿贝尔2、3组，其中？[G]满足MJD 。它们的阶数为6、12和24。鉴于Hales，Passi和Wilson的另一个结果，这完成了所有带有MJD的有限群分类的很大一部分。

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