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

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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. 
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/
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[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