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pseudovarieties of finite monoids

Proceedings of the Edinburgh Mathematical Society (1)

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On semidirectly closed non-aperiodic pseudovarieties of finite monoids
Part of
Jiří Kaďourek
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 63 / Issue 4 / November 2020

Published online by Cambridge University Press:

24 August 2020, pp. 913-928
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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.