论文标题
有限群体的非透明性的标准以及对简单组的直接正方形的识别
Criterion of nonsolvability of a finite group and recognition of direct squares of simple groups
论文作者
论文摘要
有限组$ g $的Spectrum $ω（g）$是其元素的一组订单。证明了以下足够的非透明性标准：如果在组$ g $的命令的主要除数中，则有四种不同的素数，因此$ω（g）$包含其所有成对产品，但不包含其中三个数字的产物，那么$ g $的产品则不可征收。使用此结果，我们表明，对于$ q \ geqslant 8 $和$ q \ neq 32 $，直接广场$ sz（q）\ times \ times \ times sz（q）$的szuki group $ sz（q）$唯一以$ SZ（32）$ sexters（32）$ septry为$ septrum，其特征是其频谱（32）$ seppers（32）$ seppers（32）。
The spectrum $ω(G)$ of a finite group $G$ is the set of orders of its elements. The following sufficient criterion of nonsolvability is proved: if among the prime divisors of the order of a group $G$, there are four different primes such that $ω(G)$ contains all their pairwise products but not a product of any three of these numbers, then $G$ is nonsolvable. Using this result, we show that for $q\geqslant 8$ and $q\neq 32$, the direct square $Sz(q)\times Sz(q)$ of the simple exceptional Suzuki group $Sz(q)$ is uniquely characterized by its spectrum in the class of finite groups, while for $Sz(32)\times Sz(32)$, there are exactly four finite groups with the same spectrum.
