On the Membership Problem of Finite Groups in Solvably Saturated Formations
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 559-566.

Voir la notice de l'article provenant de la source Math-Net.Ru

Theorems on the inclusion of a finite group $G$ in a solvably saturated formation $\mathfrak F$ are proved in terms of $\mathfrak F$-centrality and $c$-normality.
Keywords: saturated formation, solvably saturated formation, $\mathfrak F$-central formation, $c$-normal subgroup, Frattini extension.
@article{MZM_2012_92_4_a6,
     author = {S. F. Kamornikov and L. P. Avdashkova},
     title = {On the {Membership} {Problem} of {Finite} {Groups} in {Solvably} {Saturated} {Formations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {559--566},
     publisher = {mathdoc},
     volume = {92},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a6/}
}
TY  - JOUR
AU  - S. F. Kamornikov
AU  - L. P. Avdashkova
TI  - On the Membership Problem of Finite Groups in Solvably Saturated Formations
JO  - Matematičeskie zametki
PY  - 2012
SP  - 559
EP  - 566
VL  - 92
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a6/
LA  - ru
ID  - MZM_2012_92_4_a6
ER  - 
%0 Journal Article
%A S. F. Kamornikov
%A L. P. Avdashkova
%T On the Membership Problem of Finite Groups in Solvably Saturated Formations
%J Matematičeskie zametki
%D 2012
%P 559-566
%V 92
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a6/
%G ru
%F MZM_2012_92_4_a6
S. F. Kamornikov; L. P. Avdashkova. On the Membership Problem of Finite Groups in Solvably Saturated Formations. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 559-566. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a6/

[1] J. Buckley, “Finite groups whose minimal subgroups are normal”, Math. Z., 116:1 (1970), 15–17 | DOI | MR | Zbl

[2] S. Srinivasan, “Two sufficient conditions for supersolvability of finite groups”, Israel J. Math., 35:3 (1980), 210–214 | DOI | MR | Zbl

[3] M. Ramadan, “Influence of normality on maximal subgroups of Sylow subgroups of a finite group”, Acta Math. Hungar., 59:1-2 (1992), 107–110 | DOI | MR | Zbl

[4] M. Asaad, A. A. Heliel, “On $s$-quasinormally embedded subgroups of finite groups”, J. Pure Appl. Algebra, 165:2 (2001), 129–135 | DOI | MR | Zbl

[5] Y. Wang, “$c$-Normality of finite groups and its properties”, J. Algebra, 180:2 (1996), 954–965 | DOI | MR | Zbl

[6] H. Wei, “On $c$-normal maximal and minimal subgroups of Sylow subgroups of finite groups”, Comm. Algebra, 29:5 (2001), 2193–2200 | DOI | MR | Zbl

[7] A. N. Skiba, “A note on $c$-normal subgroups of finite groups”, Algebra Discrete Math., 2005, no. 3, 85–95 | MR | Zbl

[8] L. Miao, W. Guo, “Finite groups with some primary subgroups $\mathfrak{F}$-$s$-supplemented”, Comm. Algebra, 33:8 (2005), 2789–2800 | DOI | MR | Zbl

[9] A. N. Skiba, “On weakly $s$-permutable subgroups of finite groups”, J. Algebra, 315:1 (2007), 192–209 | DOI | MR | Zbl

[10] W. Gaschüts, “Zur Theorie der endlichen auflösbaren Gruppen”, Math. Z., 80:4 (1963), 300–305 | MR | Zbl

[11] K. Doerk, T. Hawkes, Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 | MR | Zbl

[12] L. A. Shemetkov, Formatsii konechnykh grupp, Sovremennaya algebra, Nauka, M., 1978 | MR | Zbl

[13] L. A. Shemetkov, “Stupenchatye formatsii grupp”, Matem. sb., 94:4 (1974), 628–648 | MR | Zbl

[14] L. A. Shemetkov, “Dva napravleniya v razvitii teorii neprostykh konechnykh grupp”, UMN, 30:2 (1975), 179–198 | MR | Zbl

[15] S. F. Kamornikov, “O nekotorykh svoistvakh formatsii kvazinilpotentnykh grupp”, Matem. zametki, 53:2 (1993), 71–77 | MR | Zbl

[16] V. A. Vedernikov, “O nekotorykh klassakh konechnykh grupp”, Dokl. AN BSSR, 2:10 (1988), 872–875

[17] S. F. Kamornikov, L. A. Shemetkov, “O koradikalakh subnormalnykh podgrupp”, Algebra i logika, 34:5 (1995), 493–513 | MR | Zbl