On a locality-like property of the pseudovariety J
Result description
It is well known that the pseudovariety J of all J-trivial monoids is not local, which means that the pseudovariety gJ of categories generated by J is a proper subpseudovariety of the pseudovariety lJ of categories all of whose local monoids belong to J. In this paper, it is proved that the pseudovariety J enjoys the following weaker property. For every prime number p, the pseudovariety lJ is a subpseudovariety of the pseudovariety g(J*Abp), where Abp is the pseudovariety of all elementary abelian p-groups and J*Abp is the pseudovariety of monoids generated by the class of all semidirect products of monoids from J by groups from Abp. As an application, a new proof of the celebrated equality of pseudovarieties PG=BG is obtained, where PG is the pseudovariety of monoids generated by the class of all power monoids of groups and BG is the pseudovariety of all block groups.
Keywords
Pseudovarieties of finite monoids and finite categoriesLocally finite varieties of monoids and categoriesFinitely generated relatively free monoids and categoriesSemidirect products of pseudovarieties of finite monoids
The result's identifiers
Result code in IS VaVaI
Result on the web
https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On a locality-like property of the pseudovariety J
Original language description
It is well known that the pseudovariety J of all J-trivial monoids is not local, which means that the pseudovariety gJ of categories generated by J is a proper subpseudovariety of the pseudovariety lJ of categories all of whose local monoids belong to J. In this paper, it is proved that the pseudovariety J enjoys the following weaker property. For every prime number p, the pseudovariety lJ is a subpseudovariety of the pseudovariety g(J*Abp), where Abp is the pseudovariety of all elementary abelian p-groups and J*Abp is the pseudovariety of monoids generated by the class of all semidirect products of monoids from J by groups from Abp. As an application, a new proof of the celebrated equality of pseudovarieties PG=BG is obtained, where PG is the pseudovariety of monoids generated by the class of all power monoids of groups and BG is the pseudovariety of all block groups.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Periodica mathematica Hungarica
ISSN
0031-5303
e-ISSN
1588-2829
Volume of the periodical
76
Issue of the periodical within the volume
1
Country of publishing house
HU - HUNGARY
Number of pages
46
Pages from-to
1-46
UT code for WoS article
000425544200001
EID of the result in the Scopus database
2-s2.0-85019757437
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2018