It is proved that a free solvable group of derived length at least 4 has an algorithmically undecidable universal theory.
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A. I. Mal’tsev, “Free solvable groups,” Dokl. Akad. Nauk SSSR, 130, No. 3, 495-498 (1960).
O. Chapuis, “Universal theory of certain solvable groups and bounded Ore group rings,” J. Alg., 176, No. 2, 368-391 (1995).
O. Chapuis, “∀-free metabelian groups,” J. Symb. Log., 62, No. 1, 159-174 (1997).
V. Remeslennikov and R. Stohr, “On the quasivariety generated by a non-cyclic free metabelian group,” Alg. Colloq., 11, No. 2, 191-214 (2004).
O. Chapuis, “On the theories of free solvable groups,” J. Pure Appl. Alg., 131, No. 1, 13-24 (1998).
Yu. V. Matiyasevich, “Being Diophantine for enumerable sets,” Dokl. Akad. Nauk SSSR, 191, No. 2, 279-282 (1970).
N. S. Romanovskii, “Shmel’kin embeddings for abstract and profinite groups,” Algebra Logika, 38, No. 5, 598-612 (1999).
A. G. Myasnikov and N. S. Romanovskii, “Universal theories for rigid soluble groups,” Algebra Logika, 50, No. 6, 802-821 (2011).
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Supported by RFBR, grant No. 12-01-00084.
Translated from Algebra i Logika, Vol. 51, No. 3, pp. 385-391, May-June, 2012.
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Romanovskii, N.S. Universal theories for free solvable groups. Algebra Logic 51, 259–263 (2012). https://doi.org/10.1007/s10469-012-9188-3
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DOI: https://doi.org/10.1007/s10469-012-9188-3