论文标题
$ \ textrm {sl}（n; \ mathbb {z}）$的级别$ d $ principal Alloce子组
The level $d$ principal congruence subgroup of $\textrm{SL}(n;\mathbb{Z})$
论文作者
论文摘要
Lee-Szczarba确定了$ \ textrm {sl} $ \ textrm {sl} $ \ textrm {sl}（n; \ mathbb {z}）$ d $ prive $ d $的abelianization。通过这种结果和山雀的结果，我们可以获得最小的生成集，以$γ_d（n）$。在本文中，我们给出了$γ_d（n）$的最小生成集，并确定$γ_d（n）$的Abelianization，而无需使用山雀和Lee-Szczarba的结果。此外，我们给出了三个定理，约为$γ_d（n）$。
The abelianization of the level $d$ principal congruence subgroup $Γ_d(n)$ of $\textrm{SL}(n;\mathbb{Z})$ was determined by Lee-Szczarba. By this result and a result of Tits, we can obtain a minimal generating set for $Γ_d(n)$. In this paper, we give a minimal generating set for $Γ_d(n)$ and determine the abelianization of $Γ_d(n)$, without using the results of Tits and Lee-Szczarba. Moreover, we give three theorems about $Γ_d(n)$.
