Levi classes of quasivarieties of 2-nilpotent groups
https://doi.org/10.26907/2949-3919.2025.1.64-77
Abstract
The Levi class L(M) generated by the class of groups M is the class of all groups in which the normal closure of each cyclic subgroup belongs to M.
Let p be a prime number, p ̸= 2, s be a natural number, s ≥ 2, and s > 2 for p = 3; Hps be a free group of rank 2 in the variety of nilpotent groups of class ≤ 2 of exponent ps with commutator subgroup of exponent p; Z is an infinite cyclic group; q{Hps , Z} is a quasivariety generated by the set of groups {Hps , Z}. We find a basis of quasi-identities of the Levi class L(q{Hps , Z}) and establish that there exists a continuous set of quasivarieties K such that L(K) = L(q{Hps , Z}).
About the Author
S. A. Shakhova
Altai State University
Russian Federation
Russian Federation
Svetlana Aleksandrovna Shakhova
61 Lenina av., Barnaul 656049
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Review
For citations:
Shakhova S.A. Levi classes of quasivarieties of 2-nilpotent groups. Mathematics and Theoretical Computer Science. 2025;3(1):64-77. (In Russ.) https://doi.org/10.26907/2949-3919.2025.1.64-77
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