Solvable word problems in semigroups
A semigroup \(S\) with presentation \((X;R)\) is a \(C(n)\) semigroup \((n \geq 1)\) if no \(R\)-word is a product of fewer than \(n\) pieces (a piece being a word which is a common factor of \(R\)-words in at least two distinct ways). Every finitely presented \(C(n)\) semigroup has a solvable word problem for all \(n \geq 3\) (for background and details see the reviewer's book `Techniques of Semigroup Theory' [Oxf. Univ. Press, 1982; Zbl 0744.20046]). In this paper the analogy with the small cancellation theory of groups is completed by showing that \(S\) has a solvable word problem if \(S\) is finitely presented and the presentation satisfies \(C(2)\) and \(T(4)\), where \(T(4)\) is a condition which forbids the occurrence of four particular subgraphs in the so-called star graph of the presentation.
scientific article; zbMATH DE number 736957