Rational codes and free profinite monoids
Identifieur interne : 000477 ( Main/Exploration ); précédent : 000476; suivant : 000478Rational codes and free profinite monoids
Auteurs : Jorge Almeida [Portugal, Canada] ; Benjamin Steinberg [Portugal, Canada]Source :
- Journal of the London Mathematical Society [ 0024-6107 ] ; 2009-04.
Abstract
It is well known that clopen subgroups of finitely generated free profinite groups are again finitely generated free profinite groups. Clopen submonoids of free profinite monoids need not be finitely generated nor free. Margolis, Sapir and Weil proved that the closed submonoid generated by a finite code (which is, in fact, clopen) is a free profinite monoid generated by that code. In this note we show that a clopen submonoid is free profinite if and only if it is the closure of a rational free submonoid. In this case its unique closed basis is clopen, and is, in fact, the closure of the corresponding rational code. More generally, our results apply to free pro- monoids for H an extension-closed pseudovariety of groups.
Url:
DOI: 10.1112/jlms/jdn083
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 002187
- to stream Istex, to step Curation: 002187
- to stream Istex, to step Checkpoint: 000432
- to stream Main, to step Merge: 000481
- to stream Main, to step Curation: 000477
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Rational codes and free profinite monoids</title><author wicri:is="90%"><name sortKey="Almeida, Jorge" sort="Almeida, Jorge" uniqKey="Almeida J" first="Jorge" last="Almeida">Jorge Almeida</name></author><author wicri:is="90%"><name sortKey="Steinberg, Benjamin" sort="Steinberg, Benjamin" uniqKey="Steinberg B" first="Benjamin" last="Steinberg">Benjamin Steinberg</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:A58C575BE97A0C1056B56B822E32C424232C52F1</idno><date when="2009" year="2009">2009</date><idno type="doi">10.1112/jlms/jdn083</idno><idno type="url">https://api.istex.fr/document/A58C575BE97A0C1056B56B822E32C424232C52F1/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">002187</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002187</idno><idno type="wicri:Area/Istex/Curation">002187</idno><idno type="wicri:Area/Istex/Checkpoint">000432</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000432</idno><idno type="wicri:doubleKey">0024-6107:2009:Almeida J:rational:codes:and</idno><idno type="wicri:Area/Main/Merge">000481</idno><idno type="wicri:Area/Main/Curation">000477</idno><idno type="wicri:Area/Main/Exploration">000477</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Rational codes and free profinite monoids</title><author wicri:is="90%"><name sortKey="Almeida, Jorge" sort="Almeida, Jorge" uniqKey="Almeida J" first="Jorge" last="Almeida">Jorge Almeida</name><affiliation></affiliation><affiliation></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Portugal</country></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Canada</country></affiliation></author><author wicri:is="90%"><name sortKey="Steinberg, Benjamin" sort="Steinberg, Benjamin" uniqKey="Steinberg B" first="Benjamin" last="Steinberg">Benjamin Steinberg</name><affiliation></affiliation><affiliation></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Portugal</country></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Canada</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of the London Mathematical Society</title><idno type="ISSN">0024-6107</idno><idno type="eISSN">1469-7750</idno><imprint><publisher>Oxford University Press</publisher><date type="published" when="2009-04">2009-04</date><biblScope unit="volume">79</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="465">465</biblScope><biblScope unit="page" to="477">477</biblScope></imprint><idno type="ISSN">0024-6107</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0024-6107</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract">It is well known that clopen subgroups of finitely generated free profinite groups are again finitely generated free profinite groups. Clopen submonoids of free profinite monoids need not be finitely generated nor free. Margolis, Sapir and Weil proved that the closed submonoid generated by a finite code (which is, in fact, clopen) is a free profinite monoid generated by that code. In this note we show that a clopen submonoid is free profinite if and only if it is the closure of a rational free submonoid. In this case its unique closed basis is clopen, and is, in fact, the closure of the corresponding rational code. More generally, our results apply to free pro- monoids for H an extension-closed pseudovariety of groups.</div></front></TEI><affiliations><list><country><li>Canada</li><li>Portugal</li></country></list><tree><country name="Portugal"><noRegion><name sortKey="Almeida, Jorge" sort="Almeida, Jorge" uniqKey="Almeida J" first="Jorge" last="Almeida">Jorge Almeida</name></noRegion><name sortKey="Steinberg, Benjamin" sort="Steinberg, Benjamin" uniqKey="Steinberg B" first="Benjamin" last="Steinberg">Benjamin Steinberg</name></country><country name="Canada"><noRegion><name sortKey="Almeida, Jorge" sort="Almeida, Jorge" uniqKey="Almeida J" first="Jorge" last="Almeida">Jorge Almeida</name></noRegion><name sortKey="Steinberg, Benjamin" sort="Steinberg, Benjamin" uniqKey="Steinberg B" first="Benjamin" last="Steinberg">Benjamin Steinberg</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000477 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000477 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:A58C575BE97A0C1056B56B822E32C424232C52F1
|texte= Rational codes and free profinite monoids
}}
| This area was generated with Dilib version V0.6.33. |  |