We characterise the solvable groups in the class of finite groups by an inductively defined sequence of two-variable identities. Our main theorem is the analogue of a classical theorem of Zorn which gives a characterisation of the nilpotent groups in the class of finite groups by a sequence of two-variable identities.
Bibliographical noteFunding Information:
Bandman, Kunyavski˘ı, and Plotkin were partially supported by the Ministry of Absorption (Israel), the Israeli Science Foundation founded by the Israeli Academy of Sciences – Center of Excellence Program, and the Minerva Foundation through the Emmy Noether Research Institute of Mathematics. Kunyavski˘ı and Plotkin were also supported by the RTN network HPRN-CT-2002-00287 and INTAS 00-566. Greuel and Pfister were partially supported by the DFG project “Globale Methoden in der komplexen Geometrie” as well as by the Stiftung Rheinland–Pfalz für Innovation. Greuel was also supported by the German–Israeli Foundation for Scientific Research and Development, G-616-15.6/1999.