Extending partial automorphisms and the profinite topology on free groups. (English) Zbl 0947.20018
Relations between extensions of partial automorphism of certain classes of structures and the profinite topology on free groups are studied. Among other results the authors prove a generalization of the theorem of L. Ribes and the reviewer [from Bull. Lond. Math. Soc. 25, No. 1, 37-43 (1993; Zbl 0811.20026)] stating that the product of finitely generated subgroups of a free group is closed in the profinite topology. Some interesting questions about the prosolvable topology on a free group are raised.
Reviewer: Pavel Zalesskij (Brasilia)
MSC:
| 20E05 | Free nonabelian groups |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 05C20 | Directed graphs (digraphs), tournaments |
| 08A35 | Automorphisms and endomorphisms of algebraic structures |
| 20E07 | Subgroup theorems; subgroup growth |
| 20E18 | Limits, profinite groups |
| 20E36 | Automorphisms of infinite groups |
Keywords:
partial automorphisms; profinite topologies; free groups; products of finitely generated subgroups; prosolvable topologiesCitations:
Zbl 0811.20026References:
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