Geodesic
The $\mathfrak F$-length of finite groups
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 745-754 
V. I. Kharlamova. The $\mathfrak F$-length of finite groups. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 745-754. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a9/
@article{MZM_1976_19_5_a9,
     author = {V. I. Kharlamova},
     title = {The $\mathfrak F$-length of finite groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {745--754},
     year = {1976},
     volume = {19},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a9/}
}
TY  - JOUR
AU  - V. I. Kharlamova
TI  - The $\mathfrak F$-length of finite groups
JO  - Matematičeskie zametki
PY  - 1976
SP  - 745
EP  - 754
VL  - 19
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a9/
LA  - ru
ID  - MZM_1976_19_5_a9
ER  - 
%0 Journal Article
%A V. I. Kharlamova
%T The $\mathfrak F$-length of finite groups
%J Matematičeskie zametki
%D 1976
%P 745-754
%V 19
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a9/
%G ru
%F MZM_1976_19_5_a9

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

L. A. Shemetkov [1] defined the concept of the $p$-length of an arbitrary finite group, generalizing the concept of the $p$-length of a $p$-solvable finite group of Hall–Higman [2]. In this article we introduce a more general concept of the $\mathfrak F$-length of an arbitrary finite group with respect to a certain formation $\mathfrak F$, and bounds on $\mathfrak F$-lengths and $p$-lengths are given for arbitrary finite groups.