Geodesic
On intersections of abelian and nilpotent subgroups in finite groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 128-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $A$ be an abelian subgroup of a finite group $G$, and let $B$ be a nilpotent subgroup of $G$. If $G$ is solvable, then we prove that it contains an element $g$ such that $A\bigcap B^g\le F(G)$, where $F(G)$ is the Fitting subgroup of $G$. If $G$ is not solvable, we prove that a counterexample of smallest order to the conjecture that $A\bigcap B^g\le F(G)$ for some element $g$ of $G$ is an almost simple group.
Keywords: finite group, abelian subgroup, nilpotent subgroup, intersection of subgroups, fitting subgroup. 
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V. I. Zenkov. On intersections of abelian and nilpotent subgroups in finite groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 128-131. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a13/

[1] Zenkov V.I., “Peresechenie abelevykh podgrupp v konechnykh gruppakh”, Mat. zametki, 56:1-2 (1994), 150–152 | MR | Zbl

[2] Jamali A., Viseh M., “On nilpotent subgroups containing non-trivial normal subgroups”, J. Group Theory, 3:3 (2010), 411–416 | MR | Zbl

[3] Kargapolov M.I., Merzlyakov Yu.I., Osnovy teorii grupp, Nauka, M., 1982, 288 pp. | MR

[4] Gorenstein D., Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985, 352 pp. | MR

[5] Zenkov V.I., “Peresecheniya nilpotentnykh podgrupp v konechnykh gruppakh”, Fundamental. i prikl. matematika, 2:1 (1996), 1–92 | MR | Zbl

[6] Dixon J.D., Mortimer B., Permutation groups, Springer-Verlaq, New York, 1996, 346 pp. | MR | Zbl