For each Sophie Germain prime $g\ge 5$, we construct an absolutely simple polarized abelian variety of dimension g over a finite field, whose automorphism group is a cyclic group of order $4g+2$. We also provide a description on the asymptotic behavior of prime numbers that are related to our construction.

中文翻译：

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具有最大自同构群的有限域上奇Sophie Germain素数的绝对简单极化阿贝尔变种

对于每个索菲·杰曼（Sophie Germain）素数 $G\ge 5$，我们在有限域上构造了一个绝对简单的极化g的极化阿贝尔变体，其自同构群是一个有序的循环群$4G+2$。我们还提供了与构造有关的素数的渐近行为的描述。