论文标题
在具有强嵌入统一亚组的组上
On groups with a strongly embedded unitary subgroup
论文作者
论文摘要
组$ g $的适当子组$ b $称为{\它强烈嵌入}，如果$ 2 \inπ（b）$和$ 2 \notinπ（b \ cap b^g）$ in G \ setMinus b $中的任何元素$ g \ yn_g（x）\ n_g n_g（x）\ leq b $ for ny 2-sub for ny 2-subgex in g \ setminus b $如果对于G $中的所有$ g \，子组$ \ langle a，a^g \ rangle $是有限的，则$ g $的元素$ a $称为{\ it有限}。在本文中，证明具有有限级元素$ 4 $的元素，并且在本地有限的特征性特征性$ 2 $的$ u_3（q）$ $ u_3（q）$的borel子组中，$ 2 $ $ 2 $是本地有限的，对组$ u_3（q）$等质。 关键字：统一类型的强嵌入子组，borel，cartan，互动，有限元的子组。
The proper subgroup $B$ of the group $G$ is called {\it strongly embedded}, if $2\inπ(B)$ and $2\notinπ(B \cap B^g)$ for any element $g \in G \setminus B $ and, therefore, $ N_G(X) \leq B$ for any 2-subgroup $ X \leq B $. An element $a$ of a group $G$ is called {\it finite} if for all $ g\in G $ the subgroups $ \langle a, a^g \rangle $ are finite. In the paper, it is proved that the group with finite element of order $4$ and strongly embedded subgroup isomorphic to the Borel subgroup of $U_3(Q)$ over a locally finite field $Q$ of characteristic $2$ is locally finite and isomorphic to the group $U_3(Q)$. Keywords: A strongly embedded subgroup of a unitary type, subgroups of Borel, Cartan, involution, finite element.
