Geodesic
On intersections of primary subgroups in the group \mbox{Aut}$(L_n(2))$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 105-111

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It is proved that, in a finite group $G$ whose socle is isomorphic $L_n(2)$, there exist primary subgroups $A$ and $B$ such that the intersection of $A$ and any subgroup conjugate to $B$ under the action of $G$ is nontrivial only if $G$ is isomorphic to the group Aut$(L_n(2))$; in this case, $A$ and $B$ are 2-subgroups. All ordered pairs $(A,B)$ of such subgroups are described.
Keywords: almost simple group; nilpotent subgroup. 
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     author = {V. I. Zenkov},
     title = {On intersections of primary subgroups in the group {\mbox{Aut}}$(L_n(2))$},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a9/}
}
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V. I. Zenkov. On intersections of primary subgroups in the group \mbox{Aut}$(L_n(2))$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 105-111. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a9/