Geodesic
On intersection of primary subgroups in the group $\mathrm {Aut(F_4(2))}$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 2, pp. 171-177

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It is proved that, in a finite group $G$ which is isomorphic to the group of automorphisms of the Chevalley group $F_4(2)$, there are only three possibilities for ordered pairs of primary subgroups $A$ and $B$ with condition: $A\cap B^g\ne 1$ for any $g\in G$. We describe all ordered pairs $(A,B)$ of such subgroups up to conjugacy in the group $G$ and in particular, we prove that $A$ and $B$ are $2$-groups.
Keywords: finite group, almost simple group, primary subgroup. 
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     author = {Viktor I. Zenkov and Yakov N. Nuzhin},
     title = {On intersection of primary subgroups in the group $\mathrm {Aut(F_4(2))}$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
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     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a4/}
}
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Viktor I. Zenkov; Yakov N. Nuzhin. On intersection of primary subgroups in the group $\mathrm {Aut(F_4(2))}$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 2, pp. 171-177. http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a4/