论文标题
几乎是阿贝尔群体中的理性集：语言和成长
Rational sets in virtually abelian groups: languages and growth
论文作者
论文摘要
在本文中，我们将Benson，Liardet，Evetts和Evetts＆Levine使用的结果和方法概括，以表明实际上ABELIAN G组中的合理集具有与G. G的任何生成集有关的合理（相对）增长序列。共轭代表和战争代表（任何固定子组的）等。此外，我们表明，当G在G的生成集上写入单词时，任何理性集都具有多个EDT0L表示。
In this paper we generalise and unify the results and methods used by Benson, Liardet, Evetts, and Evetts & Levine, to show that rational sets in a virtually abelian group G have rational (relative) growth series with respect to any generating set for G. We prove equivalences between the structures used in the literature, and establish the rationality of important classes of sets in G: definable sets, algebraic sets, conjugacy representatives and coset representatives (of any fixed subgroup), among others. Furthermore, we show that any rational set, when written as words over the generating set of G, has several EDT0L representations.
