This article is cited in 3 papers

On intersection of primary subgroups in the group $\mathrm {Aut(F_4(2))}$

Viktor I. Zenkov^ab, Yakov N. Nuzhin<sup>c

a</sup> Institute of Mathematics and Mechanics UB RAS, Kovalevskoi, 16, Ekaterinburg, 620990
^b Ural Federal University, Mira, 19, Ekaterinburg, 620990, Russia
^c Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: 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.

UDC: 512.542

Received: 20.05.2017
Received in revised form: 29.12.2017
Accepted: 20.01.2018

Language: English

DOI: 10.17516/1997-1397-2018-11-2-171-177

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