论文标题
与Socle $ \ mbox {}^2f_4（q^2）的几乎简单组中的共轭元素几代人
On generations by conjugate elements in almost simple groups with socle $\mbox{}^2F_4(q^2)'$
论文作者
论文摘要
我们证明，如果$ l = \ mbox {}^2f_4（2^{2n+1}）'$和$ x $是$ l $的非身份自动形态，那么$ g = \ langle l，x \ rangle $具有四个元素conjugate conjugate conjugate conjugate conjugate conjugate to $ x $ x $。该结果用于研究有限群体的$π$ - 激进的以下猜想：让$π$是所有素数集合的适当子集，让$ r $是不属于$π$的最小值。设置$ m = r $如果$ r = 2 $或$ 3 $，并设置$ m = r-1 $如果$ r \ geqslant 5 $。据说，当$π$ - radical $ \ operatatorName {o}_π（g）$中包含有限组$ g $的元素$ x $，仅当$ x $的每一个$ x $的每一个$ x $ conjugates生成$π$ -Subgroup。根据本文的结果和以前的一些结果，确认了所有有限群体的猜想，每个有限组的每个非阿比亚组成因子都是偶发，交替，线性或统一简单组或$ {}类型$ {}^2b_2^2b_2（2^2^{2n+1}）$，$，$，$，$，$，$ {2^2^2^2^2b_2（ $ {}^2f_4（2^{2n+1}）'$，$ g_2（q）$，或$ {}^3d_4（q）$。
We prove that if $L=\mbox{}^2F_4(2^{2n+1})'$ and $x$ is a nonidentity automorphism of $L$ then $G=\langle L,x\rangle$ has four elements conjugate to $x$ that generate $G$. This result is used to study the following conjecture about the $π$-radical of a finite group: Let $π$ be a proper subset of the set of all primes and let $r$ be the least prime not belonging to $π$. Set $m=r$ if $r=2$ or $3$ and set $m=r-1$ if $r\geqslant 5$. Supposedly, an element $x$ of a finite group $G$ is contained in the $π$-radical $\operatorname{O}_π(G)$ if and only if every $m$ conjugates of $x$ generate a $π$-subgroup. Based on the results of this paper and a few previous ones, the conjecture is confirmed for all finite groups whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, or unitary simple group, or to one of the groups of type ${}^2B_2(2^{2n+1})$, ${}^2G_2(3^{2n+1})$, ${}^2F_4(2^{2n+1})'$, $G_2(q)$, or ${}^3D_4(q)$.
