A note on maximal group homomorphic images of completely simple semigroups (Q1293388)

The following theorem, which is a stronger version of a result of \textit{K. S. Ajan} and \textit{F. J. Pastijn} [J. Pure Appl. Algebra 108, No. 3, 219-230 (1996; Zbl 0879.20028)] is proved. Theorem. Every finitely presented group \(G\) is the largest group homomorphic image of a Rees matrix semigroup \(S=M[F;I;J;P]\), where \(F\) is a free group of finite rank, and \(I\) and \(J\) are finite index sets. The semigroup \(S\) is finitely presented and has a solvable word problem.