Abstract
We present a solution of the Shemetkov problem (on the investigation of critical formations) for piecewise-compositional hereditary formations.
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REFERENCES
L. A. Shemetkov, “Screens of graded formations,” in: Proceedings of the Fourth All-Union Symposium on Group Theory [in Russian], Naukova Dumka, Kiev (1980), pp. 37-50.
A. N. Skiba, “On critical formations,” in: Infinite Groups and Related Algebraic Structures [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993), pp. 250-268.
V. M. Sel'kina and A. N. Skiba, “On hereditary critical functions,” Sib. Mat. Zh. 37, No. 5, 1145-1153 (1996).
V. A. Vedernikov and M. M. Sorokina, “Compositional hereditary critical formations,” Vopr. Alg. Issue 11, 6-19 (1997).
D. G. Koptyukh, “Partially compositional critical formations,” in: Abstracts of the International Conference on Symmetry in Natural Sciences Krasnoyarsk (1998), pp. 68-69.
V. A. Vedernikov and D. G. Koptyukh, “Partially compositional formations of groups,” Vopr. Alg. Issue 15 (1999).
A. Vedernikov and D. G. Koptyukh, “Ώ-compositional hereditary critical formations,” in: Abstracts of the Second International Conference on Algebra Dedicated to the Memory of Prof. Kaluzhnin Vinnitsa (1999), p. 61.
L. A. Shemetkov, Formations of Finite Groups [in Russian], Nauka, Moscow (1978).
L. A. Shemetkov and A. N. Skiba, Formations of Algebraic Systems [in Russian], Nauka, Moscow (1989).
A. N. Skiba, Algebra of Formations [in Russian], Belar. Navuka, Minsk (1997).
A. N. Skiba and L. A. Shemetkov, “On a minimal compositional screen of a compositional formation,” Vopr. Alg. Issue 7, 39-43 (1992).
H. Neumann, Varieties of Groups Springer, Berlin (1967).
V. A. Vedernikov, Elements of the Theory of Classes of Groups [in Russian], SGPI, Smolensk (1988).
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Vedernikov, V.A., Koptyukh, D.G. Hereditary Critical Ω-Compositional Formations. Ukrainian Mathematical Journal 53, 663–673 (2001). https://doi.org/10.1023/A:1012524014404
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DOI: https://doi.org/10.1023/A:1012524014404