Geodesic
On Intersections of Certain Nilpotent Subgroups in Finite Groups
Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 55-60.

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

It is proved that, in any finite group $G$ with nilpotent subgroups $A$ and $B$ and the condition $A\cap B^g\unlhd\langle A,B^g\rangle$ for any $g$ in $G$, $\operatorname{Min}_G(A,B)$ is a subgroup of $F(G)$. This generalizes the author's theorem about intersections of Abelian subgroups in a finite group, since this holds, for example, for Hamiltonian subgroups $A$ and $B$ in $G$.
Keywords: finite group, Abelian subgroup, nilpotent subgroup, intersection of subgroups, Fitting subgroup. 
@article{MZM_2022_112_1_a4,
     author = {V. I. Zenkov},
     title = {On {Intersections} of {Certain} {Nilpotent} {Subgroups} in {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {55--60},
     publisher = {mathdoc},
     volume = {112},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a4/}
}
TY  - JOUR
AU  - V. I. Zenkov
TI  - On Intersections of Certain Nilpotent Subgroups in Finite Groups
JO  - Matematičeskie zametki
PY  - 2022
SP  - 55
EP  - 60
VL  - 112
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a4/
LA  - ru
ID  - MZM_2022_112_1_a4
ER  - 
%0 Journal Article
%A V. I. Zenkov
%T On Intersections of Certain Nilpotent Subgroups in Finite Groups
%J Matematičeskie zametki
%D 2022
%P 55-60
%V 112
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a4/
%G ru
%F MZM_2022_112_1_a4
V. I. Zenkov. On Intersections of Certain Nilpotent Subgroups in Finite Groups. Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 55-60. http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a4/

[1] D. Gorenstein, Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985 | MR | Zbl

[2] V. I. Zenkov, “O peresecheniyakh primarnykh podgrupp v gruppe $\operatorname{Aut}(L_n(2))$”, Tr. IMM UrO RAN, 21, no. 1, 2015, 105–111 | MR

[3] V. V. Kabanov, A. A. Makhnev, A. I. Starostin, “Konechnye gruppy s normalnymi peresecheniyami silovskikh $2$-podgrupp”, Algebra i logika, 15:6 (1976), 655–659 | MR | Zbl

[4] V. I. Zenkov, “Peresecheniya abelevykh podgrupp v konechnykh gruppakh”, Matem. zametki, 56:2 (1994), 150–152 | MR | Zbl

[5] V. D. Mazurov, V. I. Zenkov, “O peresechenii silovskikh podgrupp v konechnykh gruppakh”, Algebra i logika, 35:4 (1996), 424–432 | MR | Zbl

[6] V. I. Zenkov, “O peresecheniyakh nilpotentnykh podgrupp v konechnykh simmetricheskikh i znakoperemennykh gruppakh”, Tr. IMM UrO RAN, 19, no. 3, 2013, 144–149 | MR

[7] I. M. Isaacs, Finite Groups Theory, Grad. Stud. Math., 92, Amer. Math. Soc., Providence, RI, 2008 | MR