Groups, the theory of ends, and context-free languages. (English) Zbl 0537.20011

This paper is devoted to the study of an interesting class of groups which are known as context-free groups. These groups possess the property that the set of all words in the alphabet of generators equivalent to the identity of the group forms a context-free language. The main results of the paper are the following. A finitely generated group is free if and only if G is context-free and torsion-free. G is virtually free if and only if G is context-free and accessible. The authors develope an interesting proof technique based on Stalling’s theorem on ends of groups.
Reviewer: A.V.Anisimov


20F05 Generators, relations, and presentations of groups
68Q45 Formal languages and automata
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20E05 Free nonabelian groups
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