Geodesic
On f-Prefrattini Subgroups
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 345-348

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

The Prefrattini subgroups of a finite soluble group were introduced by Gaschutz [3]. These are a conjugacy class of subgroups which avoid complemented chief factors and cover Frattini chief factors. Gaschutz [3, Satz 7.1] showed that if G has p-length 1 for each prime p, and if U≤G avoids all complemented chief factors and covers all Frattini factors, then U is a Prefrattini subgroup of G. We begin by proving the analogous result for the f-Prefrattini subgroups introduced by Hawkes [5], If f is a saturated formation, then the f-Prefrattini subgroups of G are a conjugacy class of subgroups which avoid f-eccentric complemented chief factors of G and cover all other chief factors of G. 
Chambers, Graham A. On f-Prefrattini Subgroups. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 345-348. doi: 10.4153/CMB-1972-062-5
@article{10_4153_CMB_1972_062_5,
     author = {Chambers, Graham A.},
     title = {On {f-Prefrattini} {Subgroups}},
     journal = {Canadian mathematical bulletin},
     pages = {345--348},
     year = {1972},
     volume = {15},
     number = {3},
     doi = {10.4153/CMB-1972-062-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-062-5/}
}
TY  - JOUR
AU  - Chambers, Graham A.
TI  - On f-Prefrattini Subgroups
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 345
EP  - 348
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-062-5/
DO  - 10.4153/CMB-1972-062-5
ID  - 10_4153_CMB_1972_062_5
ER  - 
%0 Journal Article
%A Chambers, Graham A.
%T On f-Prefrattini Subgroups
%J Canadian mathematical bulletin
%D 1972
%P 345-348
%V 15
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-062-5/
%R 10.4153/CMB-1972-062-5
%F 10_4153_CMB_1972_062_5

[1] 1. Carter, R. W. and Hawkes, T. O., The F-normalizers of a finite soluble group, J. Algebra 5 (1967), 175-202. Google Scholar

[2] 2. Chambers, G. A., p-Normally embedded subgroups of finite soluble groups, J. Algebra 16 (1970), 442-445. Google Scholar

[3] 3. Gaschutz, W., Praefrattinigruppen, Arch. Math. 13 (1962), 418-426. Google Scholar

[4] 4. Hartley, B.,On Fischer's dualization of formation theory, Proc. London Math. Soc. (3) 19 (1969), 193-207. Google Scholar

[5] 5. Hawkes, T. O., Analogues of Prefrattini subgroups, Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ. Canberra (August 1965), 145-150. Google Scholar

[6] 6. Makan, A., Another characteristic conjugacy class of subgroups of finite soluble groups, J. Austral. Math. Soc. 11 (1970), 395-400. Google Scholar

[7] 7. Mann, A., A criterion for pronormality, J. Londo. Math. Soc. 44 (1969), 175-176. Google Scholar

Cité par Sources :