Geodesic
On the intersection of maximal supersoluble subgroups of a finite group
Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 48-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The hyper-generalized-center $genz^*(G)$ of a finite group $G$ coincides with the largest term of the chain of subgroups $1=Q_0(G)\le Q_1(G)\le\ldots\le Q_t(G)\le\ldots$ where $Q_i(G)/Q_{i-1}(G)$ is the subgroup of $G/Q_{i-1}(G)$ generated by the set of all cyclic $S$-quasinormal subgroups of $G/Q_{i-1}(G)$. It is proved that for any finite group $A,$ there is a finite group $G$ such that $A\le G$ and $genz^*(G)\ne\text{Int}_\mathfrak{U}(G)$. 
@article{TIMB_2013_21_1_a5,
     author = {Wenbin Guo and Alexander N. Skiba},
     title = {On the intersection of maximal supersoluble subgroups of a finite group},
     journal = {Trudy Instituta matematiki},
     pages = {48--51},
     year = {2013},
     volume = {21},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a5/}
}
TY  - JOUR
AU  - Wenbin Guo
AU  - Alexander N. Skiba
TI  - On the intersection of maximal supersoluble subgroups of a finite group
JO  - Trudy Instituta matematiki
PY  - 2013
SP  - 48
EP  - 51
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a5/
LA  - en
ID  - TIMB_2013_21_1_a5
ER  - 
%0 Journal Article
%A Wenbin Guo
%A Alexander N. Skiba
%T On the intersection of maximal supersoluble subgroups of a finite group
%J Trudy Instituta matematiki
%D 2013
%P 48-51
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a5/
%G en
%F TIMB_2013_21_1_a5
Wenbin Guo; Alexander N. Skiba. On the intersection of maximal supersoluble subgroups of a finite group. Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 48-51. http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a5/

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

[2] Weinstein M., Between Nilpotent and Solvable, Polygonal Publishing House, 1982 | MR | Zbl

[3] Doerk K., Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin–New York, 1992 | MR

[4] Skiba A. N., “On the $\mathcal{F}$-hypercentre and the intersection of all $\mathcal{F}$-maximal subgroups of a finite group”, Journal of Pure and Applied Algebra, 216 (2012), 789–799 | DOI | MR | Zbl

[5] Guo W., Skiba A. N., “On the intersection of the $\mathfrak{F}$-maximal subgroups and the generalized $\mathfrak{F}$-hypercentre od a finite group”, J. Algebra, 366 (2012), 112–125 | DOI | MR | Zbl

[6] Baer R., “Group elements of prime power index”, Trans. Amer. Math. Soc., 75 (1953), 20–47 | DOI | MR | Zbl

[7] Agrawal R. K., “Generalized center and hypercenter of a finite group”, Proc. Amer. Math. Soc., 54 (1976), 13–21 | DOI | MR

[8] Beidleman J. C., Heineken H., “A note on intersections of maximal $\mathcal{F}$-subgroups”, J. Algebra, 333 (2010), 120–127 | DOI | MR

[9] Skiba A. N., “On the intersection of all maximal $\mathcal{F}$-subgroups of a finite group”, J. Algebra, 343 (2011), 173–182 | DOI | MR | Zbl

[10] Schmid P., “Subgroups Permutable with All Sylow Subgroups”, J. Algebra, 82 (1998), 285–293 | DOI | MR

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

[12] Shemetkov L. A., Formations of Finite Groups, Nauka, M., 1978 | MR | Zbl