Context-free pairs of groups I: Context-free pairs and graphs

Authors:
Tullio Ceccherini-Silberstein;Wolfgang Woess
Affiliations:
Dipartimento di Ingegneria, Universití del Sannio, C.so Garibaldi, 107, 82100 Benevento, Italy;Institut für Mathematische Strukturtheorie, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria
Venue:
European Journal of Combinatorics
Year:
2012

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Abstract

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.