We introduce the space of relative orders on a group and show that it is compact whenever the group is finitely generated. We use this to show that if G is a finitely generated group acting on the line by order preserving homeomorphisms and some stabilizer of a point is a proper and co-amenable subgroup, then G surjects onto ℤ. This is a generalization of a theorem of Morris.

中文翻译：

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相对阶空间和莫里斯可指示性定理的推广

我们在一个群上引入了相对阶空间，并证明只要群是有限生成的，它就是紧致的。我们用它来证明如果G是通过顺序保持同胚作用在线上的有限生成群，并且点的某个稳定器是适当且可共顺的子群，则G投射到ℤ. 这是莫里斯定理的推广。