标题： 波兰非阿基米德赋距空间的等距群 显示英文标题

标题： Isometry groups of Polish ultrametric spaces

摘要： 我们解决了Krasner在1950年代提出的长期悬而未决的问题，在波兰（即可分完备）非阿基米德空间的背景下，通过使用广义乘积的全置换群的适当形式来表征它们的等距群。由于我们的解决方案是在拓扑（波兰）群的更精细背景下开发的，因此也解决了Gao和Kechris于2003年提出的问题。此外，我们提供了属于某些自然子类的波兰非阿基米德空间的等距群与Hall、Holland和Malicki在文献中提出的各种广义乘积之间的精确对应关系。 显示英文摘要

摘要： We solve a long-standing open problem, formulated by Krasner in the 1950's, in the context of Polish (i.e. separable complete) ultrametric spaces by providing a characterization of their isometry groups using suitable forms of generalized wreath products of full permutation groups. Since our solution is developed in the finer context of topological (Polish) groups, it also solves a problem of Gao and Kechris from 2003. Furthermore, we provide an exact correspondence between the isometry groups of Polish ultrametric spaces belonging to some natural subclasses and various kinds of generalized wreath products proposed in the literature by Hall, Holland, and Malicki.