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Groups presented by finite two-monadic Church-Rosser Thue systems. (English) Zbl 0604.20034
In this interesting paper the authors give a characterization of the groups which can have a presentation by a (finite) Church-Rosser Thue system. After giving detailed and clear definitions of the concepts of Thue systems, Church-Rosser systems and monadic and special Thue systems, the authors prove their main results which says that a group G has a presentation ($$\Sigma$$ ;T) such that $$T\subseteq \Sigma^ 2\times (\Sigma \cup \{1\})$$, where $$\Sigma$$ is a finite set (of generators), is finite and Church-Rosser if and only if G is a free product of a finitely generated free group and of a finite number of finite groups. Details of the proofs or the definitions are impossible to be given here. Their main result is a refinement and an extension of an analogous result of the first two authors [Algebra, combinatorics, and logic in computer science, Colloq. Math. Soc. János Bolyai 42, 63-71 (1986)].

##### MSC:
 20F05 Generators, relations, and presentations of groups 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
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