Strongly Bounded Groups and Infinite Powers of Finite Groups
Strongly Bounded Groups and Infinite Powers of Finite Groups
复制标题
强有界群和有限群的无限幂
DOI：
10.1080/00927870600550194
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发表时间：
2004
影响因子：
0.7
通讯作者：
Yves Cornulier
中科院分区：
文献类型：
--
作者：
Yves Cornulier
我们将一个群定义为强有界的，如果它在度量空间上的每一个等距作用都有有界轨道。后一性质等价于所谓的不可数强共尾性，这是由伯格曼近期提出的。我们的主要结果是，当\(G\)是一个有限的完全群且\(I\)是任意集合时，\(G^I\)是强有界的。这强化了科佩尔伯格和蒂茨的一个结果。我们还证明了\(\omega_1\)-存在封闭群是强有界的。
We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently initiated by Bergman. Our main result is that G I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that ω1-existentially closed groups are strongly bounded.