Dynamics of implicit operations and tameness of pseudovarieties of groups (Q2750958)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Dynamics of implicit operations and tameness of pseudovarieties of groups |
scientific article; zbMATH DE number 1663201
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dynamics of implicit operations and tameness of pseudovarieties of groups |
scientific article; zbMATH DE number 1663201 |
Statements
Dynamics of implicit operations and tameness of pseudovarieties of groups (English)
0 references
21 October 2001
0 references
implicit operations
0 references
semigroups
0 references
pseudovarieties of finite groups
0 references
profinite topologies
0 references
relatively free groups
0 references
decidability
0 references
0 references
0 references
The work gives a new approach to the construction of implicit operations. For an extension closed pseudovariety of finite groups \(\mathbf V\) it is shown that if denseness of a finitely generated subgroup of a free group in the pro-\(\mathbf V\) topology is decidable, then \(\mathbf V\) is tame. In particular, it is deduced from results of \textit{L. Ribes} and the reviewer [Int. J. Algebra Comput. 4, No. 3, 359-374 (1994; Zbl 0839.20041)] that the pseudovariety of finite \(p\)-groups is tame.
0 references
