Abstract:
We prove that there exists a set RR of quasivarieties of nilpotent groups of class two any quasivariety from RR does not have an independent basis of quasi-identities to the class N2N2 of 22-nilpotent groups and has an ωω-independent basis of quasi-identities to N2N2. The intersection of all quasivarieties in RR has an independent basis of quasi-identities to N2N2. The set of such sets RR is continual.
\Bibitem{Bud19}
\by A.~I.~Budkin
\paper On the $\omega $-independence of quasivarieties of nilpotence groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 516--522
\mathnet{http://mi.mathnet.ru/semr1075}
\crossref{https://doi.org/10.33048/semi.2019.16.033}
Linking options:
https://www.mathnet.ru/eng/semr1075
https://www.mathnet.ru/eng/semr/v16/p516
This publication is cited in the following 3 articles:
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. IV. Nonstandard quasivarieties”, Siberian Math. J., 62:5 (2021), 850–858
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. III. Finitely partitionable bases”, Algebra and Logic, 59:3 (2020), 222–229
M. V. Schwidefsky, “On sufficient conditions for $Q$-universality”, Sib. elektron. matem. izv., 17 (2020), 1043–1051