Geodesic
On intersection of primary subgroups of odd order in finite almost simple groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 6, pp. 115-123

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We consider the question of the determination of subgroups $A$ and $B$ such that $A\cap B^g\ne1$ for any $g\in G$ for a finite almost simple group $G$ and its primary subgroups $A$ and $B$ of odd order. We prove that there exist only four possibilities for the ordered pair $(A,B)$. 
@article{FPM_2014_19_6_a4,
     author = {V. I. Zenkov and Ya. N. Nuzhin},
     title = {On intersection of primary subgroups of odd order in finite almost simple groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {115--123},
     publisher = {mathdoc},
     volume = {19},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2014_19_6_a4/}
}
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V. I. Zenkov; Ya. N. Nuzhin. On intersection of primary subgroups of odd order in finite almost simple groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 6, pp. 115-123. http://geodesic.mathdoc.fr/item/FPM_2014_19_6_a4/