Geodesic
Semigroups with certain finiteness conditions and Chernikov groups
Algebra and discrete mathematics, Tome 13 (2012) no. 2, pp. 299-306.

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The main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open.
Keywords: finiteness condition, epigroup, finitely assembled semigroup
Mots-clés : Chernikov group. 
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L. N. Shevrin. Semigroups with certain finiteness conditions and  Chernikov groups. Algebra and discrete mathematics, Tome 13 (2012) no. 2, pp. 299-306. http://geodesic.mathdoc.fr/item/ADM_2012_13_2_a9/

[1] Shevrin L. N., Ovsyannikov A. J., Semigroups and Their Subsemigroup Lattices, v. 1, Ural University Press, Sverdlovsk, 1990 ; v. 2, 1991 (in Russian) | MR | Zbl

[2] Shevrin L. N., Ovsyannikov A. J., Semigroups and Their Subsemigroup Lattices, Kluwer Academic Publishers, Dordrecht, 1996 | MR | Zbl

[3] Chernikov S. N., Groups with Given Properties of System of Subgroups, Nauka, Moscow, 1980 (in Russian) | MR

[4] 2nd edition, Springer-Verlag, New-York, 1979 | MR | Zbl | Zbl

[5] Robinson D. J. S., Finiteness Conditions and Generalized Soluble Groups, v. 1, 2, Springer-Verlag, Berlin, 1972

[6] Kluwer Academic Publishers, Dordrecht, 1991 | MR