Universal theories for free solvable groups.
A group \(G\) has a decidable universal theory if there is an algorithm which decides whether or not a universal sentence is true in \(G\). \textit{O. Chapuis} proved [in J. Algebra 176, No. 2, 368-391 (1995; Zbl 0860.20024)] that free metabelian groups, as well as groups close to these, have decidable universal theories. It is proved in the paper under review that a free solvable group of rank \(\geq 2\) of derived length at least 4 has undecidable universal theory. A similar question about a free solvable group of derived length 3 is still open.
scientific article; zbMATH DE number 6121538