Publication details
On a locality-like property of the pseudovariety J
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Periodica mathematica Hungarica |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf |
| 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 |
| 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. |