各种基数的强有界群
Strongly bounded groups of various cardinalities
摘要：
强有界群是这样的群，对于它们，度量空间上的每个等距作用都有有限直径的轨道。许多群都有这个性质，并且所有已知的无限群的基数至少为$2^{\aleph_0}$。我们给出了许多基数的强有界群的例子，包括$\aleph_1$，回答了Yves de Cornulier [4]的一个问题。事实上，任何无限群都嵌入为强有界群的子群，强有界群至多比强有界群大两个基数。
英文摘要：
Strongly bounded groups are those groups for which every action by isometries on a metric space has orbits of finite diameter. Many groups have been shown to have this property, and all the known infinite examples so far have cardinality at least $2^{\aleph_0}$. We produce examples of strongly bounded groups of many cardinalities, including $\aleph_1$, answering a question of Yves de Cornulier [4]. In fact, any infinite group embeds as a subgroup of a strongly bounded group which is, at most, two cardinalities larger.
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