Geodesic
On the influence of the $\mathfrak{F}$-hypercenter on the structure of finite multifactorized groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 55-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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The structure of a finite group having $t$ (normal, abnormal) subgroups with pairwise mutually coprime indices and $\mathfrak{F}$-hypercentrality constraints on pairwise intersections of these subgroups, where $\mathfrak{F}$ is a saturated formation, is described. As a consequence, new characterizations of $\Sigma_t$-closed, weakly $R_t$-closed, and $N_0$-closed formations of finite groups are established. The obtained results make a significant contribution to the solution of the question posed by W. Guo and A.N. Skiba in 2011.
Keywords: finite group, product of groups, saturated formation, $\mathfrak{F}$-hypercenter, $\mathfrak{F}$-central chief factor. 
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S. V. Balychev; V. I. Murashka. On the influence of the $\mathfrak{F}$-hypercenter on the structure of finite multifactorized groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 55-63. http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a4/

[1] Wielandt H., “Uber die Normalstrukture von mehrfach faktorisierbaren Gruppen”, B. Austral Math. Soc., 1:2 (1960), 143–146 | DOI | MR | Zbl

[2] Kegel O.H., “Zur Struktur mehrafach faktorisierbarer endlicher Gruppen”, Math. Z., 87 (1965), 409–434 | DOI | MR

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

[4] Shemetkov L.A., Formatsii konechnykh grupp, Nauka, M., 1978, 271 pp. | MR

[5] Kramer O.U., “Endliche Gruppen mit Untergruppen mit paarweise teilerfremden Indizes”, Math. Z., 139 (1974), 63–68 | DOI | MR | Zbl

[6] Guo W., Skiba A.N., “On factorizations of finite groups with $\mathfrak{F}$-hypercentral intersections of the factors”, J. Group Theory, 14 (2011), 695–708 | DOI | MR | Zbl

[7] Guo W., Structure theory for canonical classes of finite groups, Springer-Verlag, Berlin; Heidelberg, 2015, 359 pp. | DOI | MR | Zbl

[8] Kamornikov S.F., Selkin M.V., Podgruppovye funktory i klassy konechnykh grupp, Belaruskaya navuka, Mn., 2003, 254 pp.

[9] Vasilev A.F., “Formatsii i ikh raspoznavanie”, Izv. Gomel. gos. un-ta im. F. Skoriny, 2007, no. 2(41), 23–29 | MR | Zbl

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

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

[12] Vasilev A.F., Simonenko D.N., “Otnositelno radikalnye lokalnye formatsii”, Izv. Gomel. gos. un-ta im. F. Skoriny, 2006, no. 5(38), 19–25 | Zbl

[13] Monakhov V.S., Chirik I.K., “O $p$-sverkhrazreshimosti konechnoi faktorizuemoi gruppy s normalnymi somnozhitelyami”, Tr. In-ta matematiki i mekhaniki UrO RAN, 21:3 (2015), 256–267 | MR

[14] Doerk K., Hawkes T., Finite soluble groups, Walter de Gruyter, Berlin; NY, 1992, 893 pp. | MR

[15] Murashko V.I., “O proizvedeniyakh $F^*(G)$-subnormalnykh podgrupp konechnykh grupp”, Mat. zametki, 111:2 (2022), 277–286 | DOI | Zbl