Geodesic
On finite soluble groups with restrictionson cofactors of subgroups that lie in the Fitting subgroup
Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 91-97

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

Properties of finite soluble groups that depend on the orders of cofactors of subgroups that lie in the Fitting subgroup are investigated. Let n be the maximal integer such that for some prime $p$, $p^n$ divides the order of such cofactor. It is proved that the rank and the derived length of the factor group by the Frattini subgroup and the nilpotent length of a finite soluble group are bounded by certain functions of $n$. We construct examples that show that the estimates obtained are exact for groups in which cubes of primes do not divide the orders of cofactors of subgroups that lie in the Fitting subgroup. 
@article{TIMB_2020_28_1_a8,
     author = {A. A. Trofimuk},
     title = {On finite soluble groups with restrictionson cofactors of subgroups that lie in the {Fitting} subgroup},
     journal = {Trudy Instituta matematiki},
     pages = {91--97},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a8/}
}
TY  - JOUR
AU  - A. A. Trofimuk
TI  - On finite soluble groups with restrictionson cofactors of subgroups that lie in the Fitting subgroup
JO  - Trudy Instituta matematiki
PY  - 2020
SP  - 91
EP  - 97
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a8/
LA  - ru
ID  - TIMB_2020_28_1_a8
ER  - 
%0 Journal Article
%A A. A. Trofimuk
%T On finite soluble groups with restrictionson cofactors of subgroups that lie in the Fitting subgroup
%J Trudy Instituta matematiki
%D 2020
%P 91-97
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a8/
%G ru
%F TIMB_2020_28_1_a8
A. A. Trofimuk. On finite soluble groups with restrictionson cofactors of subgroups that lie in the Fitting subgroup. Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 91-97. http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a8/