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引用次数: 0
摘要
我们研究当离散的，可服从的群具有[公式:见文本]-实数秩为零的代数。众所周知，当群是局部有限时，这种情况会发生，反之则是一个开放的问题。我们证明了如果[Formula: see text]的实秩为0，那么[Formula: see text]的所有初等可服从且具有有限Hirsch长度的正规子群必然是局部有限的。
When Amenable Groups Have Real Rank Zero C*-Algebras
We investigate when discrete, amenable groups have $C^*$-algebras of real rank zero. While it is known that this happens when the group is locally finite, the converse in an open problem. We show that if $C^*(G)$ has real rank zero, then all normal subgroups of $G$ that are elementary amenable and have finite Hirsch length must be locally finite.
期刊介绍：
The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.
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