Abstract
We relate the problem of computing the closure of a finitely generated subgroup of the free group in the pro-V topology, where V is a pseudovariety of finite groups, with an extension problem for inverse automata which can be stated as follows: given partial one-to-one maps on a finite set, can they be extended into permutations generating a group in V? The two problems are equivalent when V is extension-closed. Turning to practical computations, we modify Ribes and Zalesskiǐ's algorithm to compute the pro-p closure of a finitely generated subgroup of the free group in polynomial time, and to effectively compute its pro-nilpotent closure. Finally, we apply our results to a problem in finite monoid theory, the membership problem in pseudovarieties of inverse monoids which are Mal'cev products of semilattices and a pseudovariety of groups.
| Original language | English |
|---|---|
| Pages (from-to) | 405-445 |
| Number of pages | 41 |
| Journal | International Journal of Algebra and Computation |
| Volume | 11 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2001 |
Bibliographical note
Funding Information:∗The rst and third authors received support from the French-Israeli CNRS-MOSA project Algorithmic problems on automata and semigroups. yThe rst and the second authors were supported by the NSF grant DMS-9623284. zAll three authors were supported by the Center for Communication and Information Sciences, University of Nebraska-Lincoln.
Funding
∗The rst and third authors received support from the French-Israeli CNRS-MOSA project Algorithmic problems on automata and semigroups. yThe rst and the second authors were supported by the NSF grant DMS-9623284. zAll three authors were supported by the Center for Communication and Information Sciences, University of Nebraska-Lincoln.
| Funders | Funder number |
|---|---|
| Center for Communication and Information Sciences, University of Nebraska-Lincoln | |
| National Science Foundation | DMS-9623284 |