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The level $d$ principal congruence subgroup of $\textrm{SL}(n;\mathbb{Z})$

Nao ImotoRyoma Kobayashi
Dec 2022
摘要
We give a finite generating set for the level $d$ principal congruencesubgroup $\Gamma_d(n)$ of $\textrm{SL}(n;\mathbb{Z})$. As an application, wedetermine the abelianization of $\Gamma_d(n)$. By this abelianization, itfollows that the finite generation set for $\Gamma_d(n)$ is minimal. Moreover,we give a finite presentation for $\Gamma_2(n)$.
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