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Erschienen in:
2017 | OriginalPaper | Buchkapitel
Context-Free Groups and Bass–Serre Theory
verfasst von : Volker Diekert, Armin Weiß
Erschienen in: Algorithmic and Geometric Topics Around Free Groups and Automorphisms
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The word problem of a finitely generated group is the set of words over the generators that are equal to the identity in the group. The word problem is therefore a formal language. If this language happens to be context-free, then the group is called context-free. Finitely generated virtually free groups are context-free. In the seminal paper Muller–Schupp [38] the converse was shown: every context-free group is virtually free. Over the past decades a wide range of other characterizations of context-free groups have been found. It underlines that context-free groups play a major role in combinatorial group theory.