自由时间-阿贝尔群的Stallings自动机：交集和索引
Stallings automata for free-times-abelian groups: intersections and index
摘要：
我们将经典的Stallings理论（将自由群的子群描述为自动机）扩展到自由群和阿贝尔群的直积：在引入丰富的自动机（即，自动机与额外的阿贝尔标签），我们得到一个明确的双射子群和某种类型的这种丰富的自动机，这-因为它发生在自由群-是可计算的，在生成的情况下。这种方法提供了一个整洁的几何描述（甚至非线性生成的）交叉点的非豪森家庭内的非线性生成的子群。特别地，我们给出了子群交问题和有限指标问题的几何解，分别提供了递归基和断面。
英文摘要：
We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products of free and abelian groups: after introducing enriched automata (i.e., automata with extra abelian labels), we obtain an explicit bijection between subgroups and a certain type of such enriched automata, which - as it happens in the free group - is computable in the finitely generated case. This approach provides a neat geometric description of (even non finitely generated) intersections of finitely generated subgroups within this non-Howson family. In particular, we give a geometric solution to the subgroup intersection problem and the finite index problem, providing recursive bases and transversals respectively.
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