Publication details
On semidirectly closed non-aperiodic pseudovarieties of finite monoids
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Proceedings of the Edinburgh Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BEA1B1BACC3E25204309D46CFF1E00DF/S0013091520000218a.pdf/on_semidirectly_closed_nonaperiodic_pseudovarieties_of_finite_monoids.pdf |
| Doi | http://dx.doi.org/10.1017/S0013091520000218 |
| Keywords | pseudovarieties of finite monoids; pseudovarieties of finite groups; semidirect products of monoids; semidirectly closed pseudovarieties; finite inverse monoids; finite aperiodic monoids; finite R-trivial monoids; finite p-groups; solvable groups |
| Description | It is shown that, for every prime number p, the complete lattice of all semidirectly closed pseudovarieties of finite monoids whose intersection with the pseudovariety G of all finite groups is equal to the pseudovariety Gp of all finite p-groups has the cardinality of the continuum. Furthermore, it is shown, in addition, that the complete lattice of all semidirectly closed pseudovarieties of finite monoids whose intersection with the pseudovariety G of all finite groups is equal to the pseudovariety Gsol of all finite solvable groups has also the cardinality of the continuum. |
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