Geodesic
On Nearly $S$-Permutably Embedded Subgroups of Finite Groups
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 495-505.

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

Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be $S$-permutable in $G$ if $HP=PH$ for all Sylow subgroups $P$ of $G$. A subgroup $A$ of a group $G$ is said to be $S$-permutably embedded in $G$ if for each Sylow subgroup of $A$ is also a Sylow of some $S$-permutable subgroup of $G$. In this paper, we analyze the following generalization of this concept. Let $H$ be a subgroup of a group $G$. Then we say that $H$ is nearly $S$-permutably embedded in $G$ if $G$ has a subgroup $T$ and an $S$-permutably embedded subgroup $C\le H$ such that $HT=G$ and $T\cap H\le C$. We study the structure of $G$ under the assumption that some subgroups of $G$ are nearly $S$-permutably embedded in $G$. Some known results are generalized.
Keywords: $S$-permutably embedded subgroup, saturated formation, maximal subgroup.
Mots-clés : solvable group, supersolvable group 
@article{MZM_2012_91_4_a1,
     author = {Kh. Al-Sharo},
     title = {On {Nearly} $S${-Permutably} {Embedded} {Subgroups} of {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {495--505},
     publisher = {mathdoc},
     volume = {91},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a1/}
}
TY  - JOUR
AU  - Kh. Al-Sharo
TI  - On Nearly $S$-Permutably Embedded Subgroups of Finite Groups
JO  - Matematičeskie zametki
PY  - 2012
SP  - 495
EP  - 505
VL  - 91
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a1/
LA  - ru
ID  - MZM_2012_91_4_a1
ER  - 
%0 Journal Article
%A Kh. Al-Sharo
%T On Nearly $S$-Permutably Embedded Subgroups of Finite Groups
%J Matematičeskie zametki
%D 2012
%P 495-505
%V 91
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a1/
%G ru
%F MZM_2012_91_4_a1
Kh. Al-Sharo. On Nearly $S$-Permutably Embedded Subgroups of Finite Groups. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 495-505. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a1/

[1] O. H. Kegel, “Sylow-Gruppen und Subnormalteiler endlicher Gruppen”, Math. Z., 78:1 (1962), 205–221 | DOI | MR | Zbl

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

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

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

[5] A. Ballester-Bolinches, L. M. Ezquerro, Classes of Finite Groups, Math. Appl. (Springer), 584, Springer-Verlag, Dordrecht, 2006 | DOI | MR | Zbl

[6] W. E. Deskins, “On quasinormal subgroups of finite groups”, Math. Z., 82:2 (1963), 125–132 | DOI | MR | Zbl

[7] H. Wielandt, Subnormal subgroups and permutation groups, Lectures given at the Ohio State University, Columbus, OH, 1971

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

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

[10] D. Gorenstein, Finite Groups, Harper Row Publ., New York, 1968 | MR | Zbl

[11] F. Gross, “Conjugacy of odd order Hall subgroups”, Bull. London Math. Soc., 19:4 (1987), 311–319 | DOI | MR | Zbl

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

[13] A. Shaalan, “The influence of $\pi$-quasinormality of some subgroups on the structure of a finite group”, Acta Math. Hungar., 56:3-4 (1990), 287–293 | DOI | MR | Zbl

[14] A. Ballester-Bolinches, M. C. Pedraza-Aguilera, “On minimal subgroups of finite groups”, Acta Math. Hungar., 73:4 (1996), 335–342 | DOI | MR | Zbl

[15] Y. Wang, “$c$-normality of groups and its properties”, J. Algebra, 180:3 (1996), 954–965 | DOI | MR | Zbl

[16] A. Ballester-Bolinches, Y. Wang, “Finite groups with some $C$-normal minimal subgroups”, J. Pure Appl. Algebra, 153:2 (2000), 121–127 | DOI | MR | Zbl

[17] M. Ramadan, M. Ezzat Mohamed, A. A. Heliel, “On $c$-normality of certain subgroups of prime power order of finite groups”, Arch. Math. (Basel), 85:3 (2005), 203–210 | DOI | MR | Zbl

[18] A. Ballester-Bolinches, Y. Wang, X. Guo, “$c$-supplemented subgroups of finite groups”, Glasgow Math. J., 42:3 (2000), 383–389 | DOI | MR | Zbl

[19] Y. Wang, Y. Li, J. Wang, “Finite groups with $c$-supplemented minimal subgroups”, Algebra Colloq., 10:3 (2003), 413–425 | MR | Zbl

[20] Y. Li, Y. Wang, “On $\pi$-quasinormally embedded subgroups of finite groups”, J. Algebra, 281:1 (2004), 109–123 | DOI | MR | Zbl

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

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

[23] 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

[24] A. Ballester-Bolinches, X. Guo, “On complemented subgroups of finite groups”, Arch. Math. (Basel), 72:3 (1999), 161–166 | DOI | MR | Zbl