Inverse automata and profinite topologies on a free group (Q5957776)
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scientific article; zbMATH DE number 1719031
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse automata and profinite topologies on a free group |
scientific article; zbMATH DE number 1719031 |
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Inverse automata and profinite topologies on a free group (English)
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5 September 2002
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The paper gives an elementary, self-contained proof that a finite product of finitely generated subgroups of a free group is closed in the profinite topology. Inverse automata and inverse monoid theory are used. The new result is that the product of two finitely generated subgroups of a free group is closed in the pro-\(\mathcal C\) topology, where \(\mathcal C\) is a class of finite groups closed for subgroups, quotients, finite direct products and extensions with Abelian kernel. An application to monoid theory is given.
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free groups
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profinite topology
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finite monoids
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rational subsets
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inverse automata
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pseudovarieties of finite groups
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finitely generated subgroups
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finite direct products
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