群的无星测地线语言
Star-free geodesic languages for groups
摘要：
在这篇文章中，我们证明了满足一个或两个小取消条件$C'(1/6)$和$C'(1/4)-T(4)$的有限表示的每个组具有所有测地线的集合（在同一生成集上）是无星正则语言的性质。星自由正则性的测地线集被证明是依赖于所选择的生成集，即使是自由群。我们还证明了一类群的测地集是星自由的关于一些生成集是封闭的下图（因此自由和直接）的产品，并包括几乎所有的阿贝尔群。
英文摘要：
In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions $C'(1/6)$ and $C'(1/4)-T(4)$ has the property that the set of all geodesics (over the same generating set) is a star-free regular language. Star-free regularity of the geodesic set is shown to be dependent on the generating set chosen, even for free groups. We also show that the class of groups whose geodesic sets are star-free with respect to some generating set is closed under taking graph (and hence free and direct) products, and includes all virtually abelian groups.
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。
