标题： 关于Suzuki-Ree群阶的本原素因子（修正版） 显示英文标题

标题： On primitive prime divisors of the orders of Suzuki-Ree groups (corrected version)

摘要： 已知一个著名的关于数字$2^{2m}+1$的分解，其中$m$为奇数，与简单 Suzuki 群的环面阶数有关：$2^{2m}+1$是$a=2^m+2^{(m+1)/2}+1$和$b=2^m-2^{(m+1)/2}+1$的乘积。 根据Bang-Zsigmondy定理，存在一个原始素因子 $2^{4m}-1$，即一个素数 $r$，它整除 $2^{4m}-1$ 并且对于任意 $i<4m$ 都不整除 $2^i-1$。 容易看出，$r$整除$2^{2m}+1$，因此它整除其中的一个数$a$和$b$。 本文的主要目的是证明对于每个$m>5$，$a$和$b$中的每一个都可被$2^{4m}-1$的某个本原素因子整除。 此外，我们还证明了与简单Ree群相关的本原素因子的类似结果。 作为应用，我们得到了几乎单Suzuki-Ree群的素图的独立数和2-独立数。 显示英文摘要

摘要： There is a well-known factorization of the number $2^{2m}+1$, with $m$ odd, related to the orders of tori of simple Suzuki groups: $2^{2m}+1$ is a product of $a=2^m+2^{(m+1)/2}+1$ and $b=2^m-2^{(m+1)/2}+1$. By the Bang-Zsigmondy theorem, there is a primitive prime divisor of $2^{4m}-1$, that is, a prime $r$ that divides $2^{4m}-1$ and does not divide $2^i-1$ for any $i<4m$. It is easy to see that $r$ divides $2^{2m}+1$, and so it divides one of the numbers $a$ and $b$. The main objective of this paper is to show that for every $m>5$, each of $a$ and $b$ is divisible by some primitive prime divisor of $2^{4m}-1$. Also we prove similar results for primitive prime divisors related to the simple Ree groups. As an application, we find the independence and 2-independence numbers of the prime graphs of almost simple Suzuki-Ree groups.