On the $p$-supersolvability of a finite factorizable group with normal factors
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 256-267 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain "$p$-analogs" of known criteria for the supersolvability of a finite group $G=AB$ with normal supersolvable subgroups $A$ and $B$. In addition, new sufficient conditions for the supersolvability of a finite group are found under stronger conditions than the supersolvability of normal factors.
Keywords: finite group
Mots-clés : $p$-supersolvable group, $p$-solvable group, mnp-group, t-group.
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V. S. Monakhov; I. K. Chirik. On the $p$-supersolvability of a finite factorizable group with normal factors. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 256-267. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a25/

[1] Monakhov V.S., Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006, 207 pp.

[2] Huppert B., Endliche Gruppen I, Springer, Berlin etc., 1967, 793 pp. | MR | Zbl

[3] Huppert B., “Monomialle darstellung endlicher gruppen ”, Nagoya Math. J., 3 (1953), 93–94 | MR

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

[5] Vasilev A.F., Vasileva T.I., “O konechnykh gruppakh, u kotorykh glavnye faktory yavlyayutsya prostymi gruppami”, Izv. vuzov. Matematika, 1997, no. 11(426), 10–14 | MR | Zbl

[6] Friesen D., “Products of normal supersolvable subgroups”, Proc. Amer. Math. Soc., 30:1 (1971), 46–48 | DOI | MR | Zbl

[7] Huppert B., Blackburn N., Finite groups II, Springer, Berlin etc., 1982, 531 pp. | MR | Zbl

[8] Ballester-Bolinches A., Esteban-Romero R., Asaad M., Products of finite groups, De Gruyter Expositions in Mathematics, 53, Walter de Gruyter, Berlin; New York, 2010, 334 pp. | DOI | MR | Zbl

[9] Monakhov V.S., Shpyrko O.A., “O nilpotentnoi $\pi$-dline maksimalnykh podgrupp konechnykh $\pi$-razreshimykh grupp ”, Vestn. MGU im. M.V. Lomonosova. Matematika. Mekhanika, 6 (2009), 3–8 | MR | Zbl

[10] Shemetkov L.A., Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp. | MR

[11] H.G. Bray [et al.], Between nilpotent and solvable, Polygonal Publ. House, Passaic, 1982, 231 pp. | MR

[12] Srinivasan S., “Two sufficient conditions for supersolvability of finite groups”, Israel J. Math., 35 (1980), 210–214 | DOI | MR | Zbl

[13] Asaad M., Ramadan M., Shaalan A., “Influence of $\pi$-quasinormality on maximal subgroups of Sylow subgroups of fitting subgroup of a finite group”, Arch. Math., 56 (1991), 521–527 | DOI | MR | Zbl

[14] Asaad M., Heliel A.A., “On $S$-quasinormal embedded subgroups of finite groups”, J. Pure Appl. Algebra, 165 (2001), 129–135 | DOI | MR | Zbl

[15] Ballester-Bolinches A., “Permutably embedded subgroups of finite soluble groups”, Arch. Math., 65 (1995), 1–7 | DOI | MR | Zbl

[16] Ballester-Bolinches A., Pedraza-Aguilera M.C., “Sufficient conditions for supersolvability of finite groups”, J. Pure Appl. Algebra, 127 (1998), 113–118 | DOI | MR | Zbl

[17] Monakhov V.S., Trofimuk A.A., “Finite groups with subnormal non-cyclic subgroups ”, J. Group Theory, 17:5 (2014), 889–895 | DOI | MR | Zbl

[18] Wall G.L., “Groups with maximal subgroups of Sylow subgroups normal”, Israel J. Math., 43 (1982), 166–168 | DOI | MR | Zbl

[19] Gaschutz W., “Gruppen in denen das normalteilersein transitiv ist”, J. Reine Angew. Math., 198 (1957), 87–92 | MR | Zbl

[20] Lemeshev I.V., Monakhov V.S., “Priznaki razreshimosti konechnykh grupp s ogranicheniyami na kofaktory maksimalnykh podgrupp”, Problemy fiziki, matematiki i tekhniki, 2012, no. 2(11), 88–94 | Zbl

[21] Guo W., Kondrat'ev A.S., “New examples of finite non-supersolvable groups factored by two normal supersolvable subgroups”, Internat. Conf. “Mal'tsev meeting”: collect. abstr., Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, 2012, 95

[22] Guo W., Kondratiev A.S., “Finite minimal non-supersolvable groups decomposable into the product of two normal supersolvable subgroups”, Commun. Math. Stat., 3 (2015), 285–290 | DOI | MR | Zbl

[23] Huppert B., “Normalteiler und maximale Untergruppen endlicher Gruppen”, Math. Z., 60 (1954), 409–434 | DOI | MR | Zbl

[24] Doerk K., “Minimal nicht überauflösbare, endliche Gruppen”, Math. Z., 91 (1966), 198–205 | DOI | MR | Zbl

[25] Nagrebetskii V.T., “O konechnykh minimalnykh nesverkhrazreshimykh gruppakh”, Konechnye gruppy, Nauka i tekhnika, Minsk, 1975, 104–108

[26] Ballester-Bolinches A., Esteban-Romero R., “On minimal non-supersoluble groups”, Rev. Math. Iberoamericana, 23:1 (2007), 127–142 | DOI | MR | Zbl