On Intersection of Primary Subgroups in the Group Aut(F4(2))
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https://elib.sfu-kras.ru/handle/2311/71042Author:
Zenkov, Viktor I.
Nuzhin, Yakov N.
Зенков, Виктор И.
Нужин, Яков Н.
Date:
2018-06Journal Name:
Журнал Сибирского федерального университета. Математика и физика. Journal of Siberian Federal University. Mathematics & Physics;2018 11 (2)Abstract:
It is proved that, in a finite group G which is isomorphic to the group of automorphisms of the Chevalley
group F4(2), there are only three possibilities for ordered pairs of primary subgroups A and B with
condition: A \ Bg ̸= 1 for any g 2 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. Показано, что в конечной группе G, изоморфной группе всех автоморфизмов группы Шевалле
F4(2), существуют лишь три типа упорядоченных пар примарных подгрупп A и B с условием:
A \ Bg ̸= 1 для любого g 2 G. Приведено описание всех упорядоченных пар (A;B) таких подгрупп с точностью до сопряженности в группе G, в частности, доказано, что A и B являются
2-группами
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