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Varieties of \(\ell\)-groups with infinite axiomatic rank. (English. Russian original) Zbl 0576.06018

Sib. Math. J. 26, 50-54 (1985); translation from Sib. Mat. Zh. 26, No. 1(149), 66-70 (1985).
The author constructs the variety of nilpotent metabelian lattice ordered groups of the degree 3 with infinite axiomatic rank. It is shown that the lattice of varieties of nilpotent \(\ell\)-groups of degree n (n\(\geq 3)\) has the cardinality of the continuum. There are introduced some corollaries for \(\ell\)-ordered Lie algebras.
Reviewer: B.Smarda

MSC:

06F15 Ordered groups
08B15 Lattices of varieties
17B30 Solvable, nilpotent (super)algebras
06B20 Varieties of lattices
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References:

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