Geodesic
On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups
Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 300-311.

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

A subgroup $H$ of a group $G$ is said to be an SS-quasinormal (Supplement-Sylow-quasinormal) subgroup if there is a subgroup $B$ of $G$ such that $HB = G$ and $H$ permutes with every Sylow subgroup of $B$. A subgroup $H$ of a group $G$ is said to be S-quasinormally embedded in $G$ if for every Sylow subgroup $P$ of $H$, there is an S-quasinormal subgroup $K$ in $G$ such that $P$ is also a Sylow subgroup of $K$. Groups with certain SS-quasinormal or S-quasinormally embedded subgroups of prime power order are studied.
Keywords: SS-quasinormal subgroup, $p$-nilpotent group
Mots-clés : supersolvable group, formation. 
@article{MZM_2014_95_2_a11,
     author = {Zhencai Shen and Shirong Li and Jinshan Zhang},
     title = {On {SS-Quasinormal} and {S-Quasinormally} {Embedded} {Subgroups} of {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {300--311},
     publisher = {mathdoc},
     volume = {95},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a11/}
}
TY  - JOUR
AU  - Zhencai Shen
AU  - Shirong Li
AU  - Jinshan Zhang
TI  - On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups
JO  - Matematičeskie zametki
PY  - 2014
SP  - 300
EP  - 311
VL  - 95
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a11/
LA  - ru
ID  - MZM_2014_95_2_a11
ER  - 
%0 Journal Article
%A Zhencai Shen
%A Shirong Li
%A Jinshan Zhang
%T On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups
%J Matematičeskie zametki
%D 2014
%P 300-311
%V 95
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a11/
%G ru
%F MZM_2014_95_2_a11
Zhencai Shen; Shirong Li; Jinshan Zhang. On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups. Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 300-311. http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a11/

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

[2] D. Gorenstein, Finite Groups, Harper's Ser. in Modern Math., Harper Row Publ., New York, 1968 | MR | Zbl

[3] B. Huppert, Endliche Gruppen. I, Grundlehren Math. Wiss., 134, Springer-Verlag, Berlin, 1967 | MR | Zbl

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

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

[6] A. Ballester-Bolinches, M. C. Pedraza-Aguilera, “Sufficient conditions for supersolubility of finite groups”, J. Pure Appl. Algebra, 127:2 (1998), 113–118 | DOI | MR | Zbl

[7] V. Go, A. N. Skiba, K. P. Sham, “$X$-perestanovochnye podgruppy”, Sib. matem. zhurn., 48:4 (2007), 742–759 | MR | Zbl

[8] Go Venbin, K. P. Sham, A. N. Skiba, “$G$-nakryvayuschie sistemy podgrupp dlya klassov $p$-sverkhrazreshimykh i $p$-nilpotentnykh konechnykh grupp”, Sib. matem. zhurn., 45:3 (2004), 527–539 | MR | Zbl

[9] Go Venbin, E. V. Legchekova, A. N. Skiba, “Konechnye gruppy, v kotorykh kazhdaya 3-maksimalnaya podgruppa perestanovochna so vsemi maksimalnymi podgruppami”, Matem. zametki, 86:3 (2009), 350–359 | DOI | MR | Zbl

[10] O. H. Kegel, “Sylow-Gruppen und Subnormalteiler endlicher Gruppen”, Math. Z., 78 (1962), 205–221 | DOI | MR | Zbl

[11] Sh. Li, Zh. Shen, J. Liu, X. Liu, “The influence of SS-quasinormality of some subgroups on the structure of finite groups”, J. Algebra, 319:10 (2008), 4275–4287 | DOI | MR | Zbl

[12] Sh. Li, Zh. Shen, X. Kong, “On SS-quasinormal subgroups of finite groups”, Comm. Algebra, 36:12 (2008), 4436–4447 | DOI | MR | Zbl

[13] Long Miao, “Konechnye gruppy s maksimalnymi podgruppami $\mathscr M$-dopolnyaemykh silovskikh podgrupp”, Matem. zametki, 86:5 (2009), 692–704 | DOI | MR | Zbl

[14] Y. Li, Y. Wang, “On S-quasinormally embedded subgroups of finite group”, J. Algebra, 281:1 (2004), 109–123 | DOI | MR | Zbl

[15] M. Ramadan, “The influence of S-quasinormality of some subgroups of prime power order on the structure of finite groups”, Arch. Math. (Basel), 77:2 (2001), 143–148 | DOI | MR | Zbl

[16] Zh. Shen, Sh. Li, W. Shi, “Finite groups with normally embedded subgroups”, J. Group Theory, 13:2 (2010), 257–265 | MR | Zbl

[17] Zh. Shen, W. Shi, Q. Zhang, “S-quasinormality of finite groups”, Front. Math. China, 5:2 (2010), 329–339 | DOI | MR | Zbl

[18] Zh. Shen, W. Shi, “The influence of SNS-permutability of some subgroups on the structure of finite groups”, Publ. Math. Debrecen, 78:1 (2011), 159–168 | MR | Zbl

[19] L. A. Shemetkov, A. N. Skiba, “On the $\mathscr X\Phi$-hypercentre of finite groups”, J. Algebra, 322:6 (2009), 2106–2117 | DOI | MR | Zbl

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

[21] A. N. Skiba, O. V. Titov, “Konechnye gruppy s $C$-kvazinormalnymi podgruppami”, Sib. matem. zhurn., 48:3 (2007), 674–688 | MR | Zbl

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

[23] I Syaolan, L. A. Shemetkov, “Formatsiya konechnykh grupp so sverkhrazreshimoi $\pi$-khollovoi podgruppoi”, Matem. zametki, 87:2 (2010), 280–286 | DOI | MR | Zbl