Abstract
LetL q(M) be a lattice of quasivarieties contained in a quasivarietyM. The quasivariety is closed under direct wreath Z-products if together with a group G, it contains its wreath product G ≀ Z with an infinite cyclic group Z. We prove the following: (a) ifM is closed under direct wreath Z-products then every quasivariety, which is a coatom inL q(M), is likewise closed under these; (b) ifM is closed under direct wreath products thenL q(M) has at most one coatom. An example of a quasivariety is furnished which is closed under direct wreath Z-products and whose subquasivariety lattice contains exactly one coatom. Also, it turns out that the set of quasivarieties closed under direct wreath Z-products form a complete sublatttice of the lattice of quasivarieties of groups.
Sign-in/Register to access full text options 
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 callDisclaimer: 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.
