Abstract

We denote by [Formula: see text] the implicit signature that contains the multiplication and the [Formula: see text]-power. It is proved that for any completely [Formula: see text]-reducible pseudovariety of groups [Formula: see text], the pseudovariety [Formula: see text] of all finite semigroups whose regular [Formula: see text]-classes are groups in [Formula: see text] is completely [Formula: see text]-reducible as well. The converse also holds. The tools used by Almeida, Costa, and Zeitoun for proving that the pseudovariety of all finite [Formula: see text]-trivial monoids is completely [Formula: see text]-reducible are adapted for the general setting of a pseudovariety of the form [Formula: see text].

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.