Informace o publikaci

On a locality-like property of the pseudovariety J

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KAĎOUREK Jiří

Rok publikování 2018
Druh Článek v odborném periodiku
Časopis / Zdroj Periodica mathematica Hungarica
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf
Doi http://dx.doi.org/10.1007/s10998-017-0186-z
Klíčová slova 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
Popis 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.

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