关于么半群不从其Schutzenberger群继承的性质
On properties not inherited by monoids from their Schutzenberger groups
摘要：
我们给出了一个有许多左理想和右理想的么半群的例子，其所有的Schutzenberger群都可以用有限完全重写系统表示，因此每个都有有限导子型，但是使得么半群本身没有有限导子型，因此不允许用有限完全重写系统表示。这个例子也可以作为其他几个关于完全重写系统和有限导子类型的自然问题的反例。具体地说，它允许我们构造两个等距Cayley图的生成幺半群M和N，其中N具有有限导子类型（分别允许由有限完全重写系统表示），但M不具有。这与有限生成群的有限导子类型是一个准等距不变量的情况形成对比。同样的例子也被用来表明，这两个属性都是有限的格林指数扩展下保持。
英文摘要：
We give an example of a monoid with finitely many left and right ideals, all of whose Schutzenberger groups are presentable by finite complete rewriting systems, and so each have finite derivation type, but such that the monoid itself does not have finite derivation type, and therefore does not admit a presentation by a finite complete rewriting system. The example also serves as a counterexample to several other natural questions regarding complete rewriting systems and finite derivation type. Specifically it allows us to construct two finitely generated monoids M and N with isometric Cayley graphs, where N has finite derivation type (respectively, admits a presentation by a finite complete rewriting system) but M does not. This contrasts with the case of finitely generated groups for which finite derivation type is known to be a quasi-isometry invariant. The same example is also used to show that neither of these two properties is preserved under finite Green index extensions.
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