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@article{1502220,
author = {Kaďourek, Jiří},
article_location = {Budapest},
article_number = {1},
doi = {http://dx.doi.org/10.1007/s10998-017-0186-z},
keywords = {Pseudovarieties of finite monoids and finite categories; Locally finite varieties of monoids and categories; Finitely generated relatively free monoids and categories; Semidirect products of pseudovarieties of finite monoids},
language = {eng},
issn = {0031-5303},
journal = {Periodica mathematica Hungarica},
title = {On a locality-like property of the pseudovariety J},
url = {https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf},
volume = {76},
year = {2018}
}
TY - JOUR
ID - 1502220
AU - Kaďourek, Jiří
PY - 2018
TI - On a locality-like property of the pseudovariety J
JF - Periodica mathematica Hungarica
VL - 76
IS - 1
SP - 1-46
EP - 1-46
PB - Akadémiai Kiadó
SN - 00315303
KW - Pseudovarieties of finite monoids and finite categories
KW - Locally finite varieties of monoids and categories
KW - Finitely generated relatively free monoids and categories
KW - Semidirect products of pseudovarieties of finite monoids
UR - https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf
L2 - https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf
N2 - 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.
ER -
KAĎOUREK, Jiří. On a locality-like property of the pseudovariety J. Online. \textit{Periodica mathematica Hungarica}. Budapest: Akadémiai Kiadó, 2018, roč.~76, č.~1, s.~1-46. ISSN~0031-5303. Dostupné z: https://dx.doi.org/10.1007/s10998-017-0186-z. [citováno 2024-04-23]
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