树的点集收缩与几乎稳定性定理
Retracts of vertex sets of trees and the almost stability theorem
摘要：
设G是一个群，T是一个具有有限个边稳定子的（有向）G-树，VT表示T的顶点集。我们证明了对于G-集VT的每个G-收缩V '，存在一个G-树，它的边稳定子是有限的，它的顶点集是V'。这一事实导致几乎稳定性定理的各种新的结果。我们还给出了群G、G-树T和VT的G-收缩V '使得G-树中没有顶点集V'的例子。
英文摘要：
Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V' of VT such that no G-tree has vertex set V'.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
