Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-08T00:06:53.815Z Has data issue: false hasContentIssue false

ON QUASIVARIETIES OF GROUPS AND EQUATIONS OVER GROUPS

Published online by Cambridge University Press:  08 February 2005

S. V. IVANOV
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, [email protected]
Get access

Abstract

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.

Type
Papers
Copyright
© The London Mathematical Society 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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