Geodesic
On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices~II
Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 61-64

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

The solvability of a finite group $G$ with two non-conjugate maximal subgroups $A$ and $B$ that satisfy the following requirements has been proved: subgroups $A$ and $B$ have primary indices in $G$; all proper subgroups of $A$ and $B$ are $2$-nilpotent. In addition, if $G$ is $S_4$-free and the indices of the subgroups $A$ and $B$ are coprime, then the $2$-nilpotency of the subgroups $A$ and $B$ can be replaced by their solvability.
Keywords: finite group, maximal subgroup, $2$-nilpotent subgroup, non-conjugate subgroups, primary index.
Mots-clés : solvable group 
@article{PFMT_2019_1_a10,
     author = {V. S. Monakhov and D. A. Khadanovich},
     title = {On the solvability of a finite group with a pair of non-conjugate subgroups of primary {indices~II}},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {61--64},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2019_1_a10/}
}
TY  - JOUR
AU  - V. S. Monakhov
AU  - D. A. Khadanovich
TI  - On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices~II
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2019
SP  - 61
EP  - 64
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2019_1_a10/
LA  - ru
ID  - PFMT_2019_1_a10
ER  - 
%0 Journal Article
%A V. S. Monakhov
%A D. A. Khadanovich
%T On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices~II
%J Problemy fiziki, matematiki i tehniki
%D 2019
%P 61-64
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2019_1_a10/
%G ru
%F PFMT_2019_1_a10
V. S. Monakhov; D. A. Khadanovich. On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices~II. Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 61-64. http://geodesic.mathdoc.fr/item/PFMT_2019_1_a10/