Geodesic
On F-subnormal subgroups and Frattini-like subgroups of a finite group
Glasgow mathematical journal, Tome 36 (1994) no. 2, pp. 241-247

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout the paper we consider only finite groups.J. C. Beidleman and H. Smith [3] have proposed the following question: “If G is a group and Ha subnormal subgroup of G containing Φ(G), the Frattini subgroup of G, such that H/Φ(G)is supersoluble, is H necessarily supersoluble? “In this paper, we give not only an affirmative answer to this question but also we see that the above result still holds if supersoluble is replaced by any saturated formation containing the class of all nilpotent groups. 
Ballester-Bolinches, A.; Pérez-Ramos, M. D. On F-subnormal subgroups and Frattini-like subgroups of a finite group. Glasgow mathematical journal, Tome 36 (1994) no. 2, pp. 241-247. doi: 10.1017/S0017089500030780
@article{10_1017_S0017089500030780,
     author = {Ballester-Bolinches, A. and P\'erez-Ramos, M. D.},
     title = {On {F-subnormal} subgroups and {Frattini-like} subgroups of a finite group},
     journal = {Glasgow mathematical journal},
     pages = {241--247},
     year = {1994},
     volume = {36},
     number = {2},
     doi = {10.1017/S0017089500030780},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500030780/}
}
TY  - JOUR
AU  - Ballester-Bolinches, A.
AU  - Pérez-Ramos, M. D.
TI  - On F-subnormal subgroups and Frattini-like subgroups of a finite group
JO  - Glasgow mathematical journal
PY  - 1994
SP  - 241
EP  - 247
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500030780/
DO  - 10.1017/S0017089500030780
ID  - 10_1017_S0017089500030780
ER  - 
%0 Journal Article
%A Ballester-Bolinches, A.
%A Pérez-Ramos, M. D.
%T On F-subnormal subgroups and Frattini-like subgroups of a finite group
%J Glasgow mathematical journal
%D 1994
%P 241-247
%V 36
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500030780/
%R 10.1017/S0017089500030780
%F 10_1017_S0017089500030780

[1] 1.Ballester-Bolinches, A., Maximal subgroups and formations. J. Pure Appl. Algebra 61 (1989), 223–232. Google Scholar

[2] 2.Ballester-Bolinches, A., Doerk, K. and Pérez-Ramos, M. D., On 𝓕normal subgroups of finite soluble groups, preprint. Google Scholar

[3] 3.Beidleman, J. C. and Smith, H., On Frattini-like subgroups, Glasgow Math. J. 35 (1993), 95–98. Google Scholar

[4] 4.Bhattacharya, P. and Mukherjee, N. P., On the intersection of a class of maximal subgroups of a finite group II, J. Pure Appl. Algebra 42 (1986), 117–124. Google Scholar

[5] 5.Doerk, K. and Hawkes, T. O., Finite soluble groups (De Gruyter, Berlin-New York, 1992). Google Scholar

[6] 6.Feng, Y. and Zhang, B., Frattini subgroups relative to formation functions, J. Pure Appl. Algebra 64 (1990), 145–148. Google Scholar

[7] 7.Förster, P., On finite groups all of whose subgroups are 𝓕-subnormal or 𝓕subabnormal, J. Algebra 103 (1986), 285–293. Google Scholar

[8] 8.Griess, R. L. and Schmid, P., The Frattini module, Arch. Math. 30 (1978), 256–266. Google Scholar

[9] 9.Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, 1967). Google Scholar

Cité par Sources :