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Bulletin of the London Mathematical Society 2005 37(1):67-74; doi:10.1112/S0024609304003820
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© London Mathematical Society

On Quasivarieties of Groups and Equations Over Groups

S. V. Ivanov

Department of Mathematics, University of Illinois Urbana, IL 61801, USA; ivanov{at}math.uiuc.edu

Received 1 October 2002. Revision received 5 May 2004.

A proof is given that the quasivariety of groups generated by finite and torsion-free groups does not contain the class of periodic groups. This result is related to (and inspired by) the solvability of equations over groups. The proof uses the Feit–Thompson theorem on the solvability of finite groups of odd order as well as Kostrikin–Zelmanov results on the restricted Burnside problem, and applies technical details of a recent construction of weakly finitely presented periodic groups. 2000 Mathematics Subject Classification 20E06, 20F05, 20F06, 20F50 (primary).

Supported in part by NSF grants DMS 98-01500 and DMS 00-99612.


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