Let G be a finitely generated group, A a finite set of generators and K a subgroup of G. We define what it means for (G, K) to be a context-free pair; when K is trivial, this specializes to the standard definition of G to be a context-free group.We derive some basic properties of such group pairs. Context-freeness is independent of the choice of the generating set. It is preserved under finite index modifications of G and finite index enlargements of K. If G is virtually free and K is finitely generated then (G, K) is context-free. A basic tool is the following: (G, K) is context-free if and only if the Schreier graph of (G, K) with respect to A is a context-free graph.
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机译：假设G是一个有限生成的组，A是一个有限的生成器集合，K是G的一个子组。我们定义（G，K）为上下文无关的对的含义;当K不重要时，这专门针对G的标准定义是上下文无关的组。我们推导了此类组对的一些基本属性。上下文无关性独立于生成集的选择。它是在G的有限索引修改和K的有限索引扩大下保留的。如果G实际上是自由的并且K是有限生成的，则（G，K）是上下文无关的。基本工具如下：（G，K）仅当（ G ， K ）的Schreier图相对于 A时是上下文无关的是无上下文图。
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