Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T03:29:52.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Tarski's problem for varieties of groups with a commutator identity

Published online by Cambridge University Press:  12 March 2014

John Lawrence
John Lawrence*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

It is proved that for a variety of groups in which the relatively free groups are solvable, the relatively free groups of distinct finite rank are not elementarily equivalent.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 51 , Issue 1 , March 1986 , pp. 75 - 78
Copyright
Copyright © Association for Symbolic Logic 1986

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.)

References

REFERENCE

[1]Rogers, P., Smith, H. and Solitar, D., Tarski's problem for solvable groups (to appear).Google Scholar
[2]Szmielew, W., Elementary properties of Abelian groups, Fundamenta Mathematicae, vol. 41 (1955), pp. 203–271.Google Scholar
[3]Tarski, A., Some notions on the borderline of algebra and metamathematics, Proceedings of the International Congress of Mathematicians (Cambridge, Massachusetts, 1950), vol. 1, American Mathematical Society, Providence, Rhode Island, 1952, pp. 705–720.Google Scholar
[4]Vaughan-Lee, R., Uncountably many varieties of groups, Bulletin of the London Mathematical Society, vol. 2 (1970), pp. 280–286.Google Scholar