Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extending partial automorphisms
and the profinite topology on free groups


Authors: Bernhard Herwig and Daniel Lascar
Journal: Trans. Amer. Math. Soc. 352 (2000), 1985-2021
MSC (2000): Primary 20E05, 05C25; Secondary 05C20, 08A35
Published electronically: October 21, 1999
MathSciNet review: 1621745
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A class of structures $\mathcal{C}$ is said to have the extension property for partial automorphisms (EPPA) if, whenever $C_1$ and $C_2$ are structures in $\mathcal{C}$, $C_1$ finite, $C_1\subseteq C_2$, and $p_1,p_2,\dotsc,p_n$ are partial automorphisms of $C_1$ extending to automorphisms of $C_2$, then there exist a finite structure $C_3$ in $\mathcal{C}$ and automorphisms $\alpha _1, \alpha _2,\dotsc,\alpha _n$ of $C_3$ extending the $p_i$. We will prove that some classes of structures have the EPPA and show the equivalence of these kinds of results with problems related with the profinite topology on free groups. In particular, we will give a generalisation of the theorem, due to Ribes and Zalesskii stating that a finite product of finitely generated subgroups is closed for this topology.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20E05, 05C25, 05C20, 08A35

Retrieve articles in all journals with MSC (2000): 20E05, 05C25, 05C20, 08A35


Additional Information

Bernhard Herwig
Affiliation: Institut für Mathematische Logik, Universität Freiburg, D-79104 Freiburg, Germany
Email: herwig@sun2.ruf.uni.freiburg.de

Daniel Lascar
Affiliation: Université Paris 7, CNRS, UPRESA 7056, UFR de Mathématiques, 2 Place Jussieu, Case 7012, 75251, Paris CEDEX 05, France
Email: lascar@logique.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02374-0
PII: S 0002-9947(99)02374-0
Keywords: Partial isomorphisms, profinite topology, finite structures, extension problem
Received by editor(s): October 30, 1997
Published electronically: October 21, 1999
Article copyright: © Copyright 2000 American Mathematical Society