$J$-construction of composition formations and products of finite groups
Problemy fiziki, matematiki i tehniki, no. 4 (2016), pp. 68-73.

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In [1] $J$-construction of composition formations was introduced. Some properties of them were found and applications to the study of products of normal and mutually permutable subgroups were obtained. In this paper we continue investigation in this area.
Keywords: finite group, $Jc$-supersoluble group, $Jca$-supersoluble group, product of normal subgroups, mutually permutable product
Mots-clés : $J$-quasinilpotent group, $Jca$-soluble group, composition formation.
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E. N. Myslovets. $J$-construction of composition formations and products of finite groups. Problemy fiziki, matematiki i tehniki, no. 4 (2016), pp. 68-73. http://geodesic.mathdoc.fr/item/PFMT_2016_4_a11/

[1] A. F. Vasil'ev, T. I. Vasil'eva, E. N. Myslovets, “On finite groups with a given normal structure”, Siberian Electronic Mathematical Reports, 13 (2016), 897–910 | MR

[2] V. A. Vedernikov, “On some classes of finite groups”, Dokl. Akad. Nauk BSSR, 32:10 (1988), 872–875 | MR | Zbl

[3] W. Guo, A. N. Skiba, “On finite quazi-$\mathfrak{F}$-groups”, Communication in Algebra, 37 (2009), 470–481 | DOI | MR | Zbl

[4] W. Guo, A. N. Skiba, “On some classes of finite quazi-$\mathfrak{F}$-groups”, Journal of Group Theory, 12 (2009), 407–417 | DOI | MR | Zbl

[5] E. P. Vdovin, D. O. Revin, L. A. Shemetkov, “Formations of finite $C_{\pi}$-groups”, St. Petersburg Math. J., 24 (2013), 29–37 | DOI | MR | Zbl

[6] A. F. Vasil'ev, T. I. Vasil'eva, “On finite groups whose principal factors are simple groups”, Russian Mathematics (Izvestiya VUZ. Matematika), 41:11 (1997), 8–12 | MR | Zbl

[7] D. J. S. Robinson, “The structure of finite groups in which permutability is a transitive relation”, J. Austral. Math. Soc., 70 (2001), 143–149 | DOI | MR

[8] A. Ballester-Bolinches, J. Cossey, “Totally permutable products of finite groups satisfying SC and PST”, Monatsh. Math., 145 (2005), 89–94 | DOI | MR | Zbl

[9] J. C. Beidleman, P. Hauck, H. Heineken, “Totally permutable products of certain classes of finite groups”, J. Algebra, 276 (2004), 826–835 | DOI | MR | Zbl

[10] A. Ballester-Bolinches, J. Cossey, M. C. Pedraza-Aguilera, “On mutually permutable products of finite groups”, J. Algebra, 294 (2005), 127–135 | DOI | MR | Zbl

[11] R. Baer, “Classes of finite groups and their properties”, Illinois J. Math., 1:2 (1957), 115–187 | MR | Zbl

[12] H. G. Bray et al., Between Nilpotent and Solvable, ed. M. Weinstein, Polugonal Publishing House, Passaic, 1982, 240 pp. | MR | Zbl

[13] V. S. Monakhov, I. K. Chirik, “On the $p$-supersolvability of a finite factorizable group with normal factors”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 3, 2015, 256–267 | MR

[14] E. N. Myslovets, “On products of normal generalized supersoluble subgroups of finite groups”, Izv. of F. Scorina Gomel State University, 6:75 (2012), 163–167

[15] A. Ballester-Bolinches, R. Esteban-Romero, M. Asaad, Products of Finite Groups, Walter de Gruyter, Berlin, 2010, 334 pp. | MR | Zbl

[16] E. N. Myslovets, “On mutually permutable products of generalized supersoluble subgroups of finite groups”, Asian-European Journal of Matematics, 9:2 (2016), 1650054-1–1650054-10 | DOI | MR

[17] J. C. Beidleman, H. Heineken, “Mutually permutable subgroups and group classes”, Arch. Math., 85 (2005), 12–30 | DOI | MR

[18] J. C. Beidleman, H. Heineken, “Group classes and mutually permutable products”, Journal of Algebra, 297 (2006), 409–416 | DOI | MR | Zbl

[19] L. A. Shemetkov, Formations of finite groups, Nauka, M., 1978, 272 pp. | MR | Zbl

[20] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992, 891 pp. | MR

[21] A. N. Skiba, L. A. Shemetkov, “Multiply $\mathfrak{L}$-composition formations of finite groups”, Ukrainsk. Math. Zh., 52:6 (2000), 783–797 (In Russian) | MR | Zbl