Closed Subgroups in Pro-V Topologies and the Extension Problem for Inverse Automata

نویسندگان

  • Stuart W. Margolis
  • Mark V. Sapir
  • Pascal Weil
چکیده

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 Zalesskĭı’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.

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عنوان ژورنال:
  • IJAC

دوره 11  شماره 

صفحات  -

تاریخ انتشار 2001