This article is cited in 7 scientific papers (total in 7 papers)
Some questions in the theory of varieties of groups
Yu. G. Kleiman
In this paper a new method of studying identity relations in groups is described. Among the results obtained by this method is an example of a group variety that does not have an independent basis of identities. A conjecture by P. Hall on marginal subgroups is refuted. The question of the relation between the representation of a group variety in the form of a union and the product of two proper subvarieties is considered. An example of a group variety having a set of continuum many different covering varieties is constructed and a number of results are obtained, as corollaries, on whether (solvable) group varieties can be generated by certain classes of groups.
Bibliography: 26 titles.
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Mathematics of the USSR-Izvestiya, 1984, 22:1, 33–65
MSC: Primary 20E10; Secondary 20E05, 20E26, 20F16
Yu. G. Kleiman, “Some questions in the theory of varieties of groups”, Izv. Akad. Nauk SSSR Ser. Mat., 47:1 (1983), 37–74; Math. USSR-Izv., 22:1 (1984), 33–65
Citation in format AMSBIB
\paper Some questions in the theory of varieties of groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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M. I. Anokhin, “A basis of identities of a variety generated by a finitely-based quasi-variety of groups”, Sb. Math., 189:8 (1998), 1115–1124
M. I. Anokhin, “Embedding lattices in lattices of varieties of groups”, Izv. Math., 63:4 (1999), 649–665
V. Yu. Popov, “A Ring Variety without an Independent Basis”, Math. Notes, 69:5 (2001), 657–673
V. Yu. Popov, “O nezavisimo baziruemykh mnogoobraziyakh monoidov”, Fundament. i prikl. matem., 8:3 (2002), 829–876
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V. Yu. Popov, “The Property of Having Independent Basis in Semigroup Varieties”, Algebra and Logic, 44:1 (2005), 46–54
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