哥德巴赫猜想的群论注记
Group-theoretic remarks on Goldbach's conjecture
摘要：
著名的强二进制哥德巴赫猜想断言，每个偶数$2n \geq 8$总是可以表示为两个不同的奇素数之和。我们使用一种新的方法来处理这个猜想。特别地，我们应用$2n$和$2n-1$度交替群的元素阶素图刻画了这个猜想，并给出了它的六个群论版本;进一步证明了当$p \geq 11$是素数时，这个猜想对$p+1$和$p-1$都成立.
英文摘要：
The famous strongly binary Goldbach's conjecture asserts that every even number $2n \geq 8$ can always be expressible as the sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we apply the element order prime graphs of alternating groups of degrees $2n$ and $2n-1$ to characterize this conjecture, and present its six group-theoretic versions; and further prove that this conjecture is true for $p+1$ and $p-1$ whenever $p \geq 11$ is a prime number.
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