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About varieties of weakly abelian \(\ell\)-groups. (English) Zbl 0769.06009
The author answers the question if the equality \(W_ a=\bigcup^ \infty_{n=1} N_ n\) is true. Where \(N_ n\) is the variety of all nilpotent \(\ell\)-groups of class \(n\) and \(W_ a\) is the variety of all weakly Abelian \(\ell\)-groups. Further he constructs a variety of weakly Abelian \(\ell\)-groups for every prime \(p\) which is not generated by the set of its nilpotent \(\ell\)-groups.

MSC:
06F15 Ordered groups
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References:
[1] MARTINEZ J.: Free products in varieties of lattice ordered groups. Czechoslovak Math. J. 22(97) (1972), 535-553. · Zbl 0247.06022
[2] KOPYTOV V. M.: Lattice ordered locally nilpotent groups. Algebra i Logika 14 (1975), 407-413. · Zbl 0356.06024
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[4] MAĽCEV A. I.: Nilpotent torsion-free groups. Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 201-212.
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