Use this identifier to quote or link this document: http://hdl.handle.net/2072/1190

Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms
Ciobanu, Laura; Dicks, Warren
Centre de Recerca Matemàtica
Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.
2005-09
Automorfismes
Grups lliures
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/)
Preprint
Centre de Recerca Matemàtica
Prepublicacions del Centre de Recerca Matemàtica;645
         

Full text files in this document

Files Size Format
Pr645.pdf 104.1 KB PDF

Show full item record

 

Coordination

 

Supporters