Two examples in the Galois theory of free groups

JOURNAL OF ALGEBRA

卷:305

Article

Ciobanu, Laura ; Dicks, Warren

关键词: free group;    automorphism;    retract;    fixed subgroup;   

DOI  :  10.1016/j.jalgebra.2006.02.029

来源: Elsevier

【 摘 要 】

Let F be a free group, and let H be a subgroup of F. The 'Galois monoid' End(H)(F) consists of all endomorphisms of F which fix every element of H; the 'Galois group' Aut(H) (F) consists of all automorphisms of F which fix every element of H. The End(F)-closure and the Aut(F)-closure of H are the fixed subgroups, Fix(EndH (F)) and Fix(Aut(H) (F)), respectively. Martino and Ventura considered examples where Fix(Aut(H) (F)) not equal Fix (End(H) (F)) = H. We obtain, for two of their examples, explicit descriptions of EndH (F), AutH (F), and Fix(Aut(H) (F)), and, hence, give much simpler verifications that Fix(Aut(H) (F)) not equal Fix(End(H) (F)), in these cases. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free