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Krasil’nikov, A. N.; Shmel’kin, A. L.

On the Specht property and the basic rank of some products of group varieties. (English. Russian original) Zbl 0529.20016

Algebra Logic 20, 357-363 (1982); translation from Algebra Logika 20, 546-554 (1981).
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MSC:

20E10 Quasivarieties and varieties of groups
08B05 Equational logic, Mal’tsev conditions
20F16 Solvable groups, supersolvable groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)

Keywords:

varieties of groups; finite basis property; partially well ordered sets; basic rank; nilpotent wreath product; supersoluble group; finitely based variety; variety of nilpotent groups; locally finite variety
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References:

[1] A. Yu. Ol’shanskii, ”On the finite basis problem for groups,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 3, 376–384 (1970).
[2] R. M. Bryant and M. F. Newman, ”Some finitely based varieties of groups,” Proc. London Math. Soc.,28, No. 2, 237–252 (1974). · Zbl 0278.20020 · doi:10.1112/plms/s3-28.2.237
[3] A. L. Shmel’kin, ”Wreath products and varieties of groups,” Izv. Akad. Nauk SSSR, Ser. Mat.,29, No. 1, 149–170 (1965). · Zbl 0135.04701
[4] G. Higman, ”Ordering by divisibility in abstract algebras,” Proc. London Math. Soc.,2, No. 7, 326–336 (1952). · Zbl 0047.03402 · doi:10.1112/plms/s3-2.1.326
[5] H. Neumann, Varieties of Groups, Ergeb. Math. Grenz. (N.F.), Band 37, Springer-Verlag, New York (1967). · Zbl 0149.26704
[6] G. Baumslag, ”On the residual nilpotence of some varietal products,” Trans. Am. Math. Soc.,109, No. 2, 357–365 (1963). · Zbl 0118.03501 · doi:10.1090/S0002-9947-1963-0155888-0
[7] Yu. V. Kuz’min, ”Representations of finite groups by automorphisms of nilpotent almost spaces and automorphisms of nilpotent groups,” Sib. Mat. Zh.,13, No. 1, 107–117 (1972). · Zbl 0229.20007
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