Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T16:05:30.271Z Has data issue: false hasContentIssue false
  • English
  • Français

UNCOUNTABLE HOMOMORPHIC IMAGES OF POLISH GROUPS ARE NOT $\aleph _{1}$-FREE GROUPS

Published online by Cambridge University Press:  08 February 2005

ANATOLE KHELIF
ANATOLE KHELIF
Affiliation:
Equipe de Logique Mathématique, Université Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France e-mail: khelif@logique.jussieu.fr
Get access

Abstract

Shelah has recently proved that an uncountable free group cannot be the automorphism group of a countable structure. In fact, he proved a more general result: an uncountable free group cannot be a Polish group. A natural question is: can an uncountable $\aleph _{1}$-free group be a Polish group? A negative answer is given here; indeed, it is proved that an $\aleph _{1}$-free group cannot be a homomorphic image of a Polish group. In fact, a stronger result is proved, involving a non-commutative analogue of the notion of separable group.

Keywords

20E05
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 1 , January 2005 , pp. 54 - 60
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.)