\(\mathbf{PG}=\mathbf{BG}\): redux (Q2709047)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\mathbf{PG}=\mathbf{BG}\): redux |
scientific article |
Statements
7 April 2002
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inverse automata
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profinite topologies
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Malcev products
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\(\mathcal J\)-trivial semigroups
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semidirect products
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block groups
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power groups
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\(\mathbf{PG}=\mathbf{BG}\): redux (English)
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This paper serves as a taster for the topological theory of inverse automata of the author. Here, he develops the theory (which makes use of the closure of products of finitely generated subgroups of the free group in the profinite topology) to give a relatively short proof of a theorem of Henckell and Rhodes that every block group (that is, member of the variety generated by Malcev products of \(\mathcal J\)-trivial semigroups and groups) lies in the variety generated by semidirect products of the same pair of classes. -- This is often expressed as \(\text{PG}=\text{BG}\): block groups form the variety generated by power groups.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00028].
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