$S$-$C$-permutably embedded subgroups of finite groups
Problemy fiziki, matematiki i tehniki, no. 3 (2010), pp. 41-48.

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

A subgroup $H$ of a finite group $G$ is said to be $s$-conditionally permutably embedded (or in brevity, $s$-$c$-permutably embedded) in $G$ if for each $p \in \pi(H)$ every Sylow $p$-subgroup of $H$ is a Sylow $p$-subgroup of some $s$-conditionally permutable subgroup of $G$. In this paper, we use some $s$-$c$-permutably embedded subgroups to study the structure of some groups. Some known results are generalized.
Keywords: finite group, $s$-conditionally permutably embedded subgroup, Sylow subgroup, maximal subgroup.
Mots-clés : formation
@article{PFMT_2010_3_a5,
     author = {Jianhong Huang and Fengyan Xie and Xiaolan Yi},
     title = {$S$-$C$-permutably embedded subgroups of finite groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {41--48},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2010_3_a5/}
}
TY  - JOUR
AU  - Jianhong Huang
AU  - Fengyan Xie
AU  - Xiaolan Yi
TI  - $S$-$C$-permutably embedded subgroups of finite groups
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2010
SP  - 41
EP  - 48
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2010_3_a5/
LA  - ru
ID  - PFMT_2010_3_a5
ER  - 
%0 Journal Article
%A Jianhong Huang
%A Fengyan Xie
%A Xiaolan Yi
%T $S$-$C$-permutably embedded subgroups of finite groups
%J Problemy fiziki, matematiki i tehniki
%D 2010
%P 41-48
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2010_3_a5/
%G ru
%F PFMT_2010_3_a5
Jianhong Huang; Fengyan Xie; Xiaolan Yi. $S$-$C$-permutably embedded subgroups of finite groups. Problemy fiziki, matematiki i tehniki, no. 3 (2010), pp. 41-48. http://geodesic.mathdoc.fr/item/PFMT_2010_3_a5/

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

[2] W. Guo, The Theory of Class of Groups, Science Press-Kluwer Academic Publishers, Beijing–New-York–Dordrecht–Boston, 2000 | MR

[3] O. Ore, “Contributions to the theory of groups of finite order”, Duke Math. J., 5:2 (1939), 431–460 | DOI | MR

[4] N. Itô, J. Szép, “Uber die Quasinormalteiler endlicher Gruppen”, Act. Sci. Math., 23 (1962), 168–170 | MR | Zbl

[5] W. Guo, K. P. Shum, A. N. Skiba, “Conditionally permutable subgroups and supersolubility of finite groups”, Southeast Asian Bull. Math., 29:2 (2005), 493–510 | MR | Zbl

[6] W. Guo, K. P. Shum, A. N. Skiba, “$X$-quasinormal subgroups”, Siberian Math. J., 48:1 (2004), 433–442 | DOI | MR | Zbl

[7] W. Guo, K. P. Shum, A. N. Skiba, “Criterions of supersolubility for products of supersoluble groups”, Publ. Math. Debrecen, 68:3–4 (2006), 433–449 | MR | Zbl

[8] W. Guo, K. P. Shum, A. N. Skiba, “$X$-semipermutable subgroups of finite groups”, J. Algebra, 315 (2007), 31–41 | DOI | MR | Zbl

[9] J. Huang, W. Guo, “$S$-conditionally permutable subgroups of finite groups”, Chin. Ann. Math. A, 28:1 (2007), 17–26 (in chinese) | MR | Zbl

[10] S. Chen, W. Guo, “$S$-$C$-Permutably Embedded Subgroups of Finite Groups”, Int. J. Contemp. Math. Science, 3:20 (2008), 951–960 | MR | Zbl

[11] W. Guo, K. P. Shum, A. N. Skiba, “$G$-covering systems of subgroups for classes of $p$-supersoluble and $p$-nilpotent finite groups”, Siberian Math. J., 45:3 (2004), 433–442 | DOI | MR | Zbl

[12] Y. Wang, “Finite groups with some subgroups of Sylow subgroups $c$-supplemented”, J. Algebra, 224 (2000), 464–478 | DOI | MR

[13] B. Huppert, Endliche Gruppen, v. I, Springer-Verlag, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[14] W. Guo, “On $\mathfrak{F}$-supplement subgroups of finite groups”, Manuscripta Math., 127 (2008), 139–150 | DOI | MR | Zbl

[15] Y. Wang, H. Wei, Y. Li, “A generalization of Kramer's theorem and its applications”, Bull. Austral. Math. Soc., 65 (2002), 467–475, Research is supported by NNSF Grant of China (Grant: 10771180) | DOI | MR | Zbl

[16] J. S. Robinson Derek, A Course in the Theory of Groups, Springer-Verlag, New York–Heidelberg–Berlin, 1982 | MR

[17] B. Hu, W. Guo, “$C$-semipermutable subgroups of finite groups”, Siberian Math. J., 48:1 (2007), 180–188 | DOI | MR | Zbl

[18] M. Zha, W. Guo, B. Li, “On $p$-supersolubility of finite groups”, J. of Math. (PRC), 20:5 (2007), 563–568 (in chinese) | MR

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

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

[21] M. Asaad, “On maximal subgroups of Sylow subgroups of finite groups”, Comm. Algebra, 26:11 (1998), 3647–3652 | DOI | MR | Zbl

[22] G. Chen, J. Li, “The influence of $X$-semipermutability of subgroups on the structure of finite groups”, Science in China Series A: Mathematics, 52:2 (2009), 261–271 | DOI | MR | Zbl