Wohlfahrt's Theorem and index formula for elementary matrix groups and $SL(2, \mathcal O)$

The present article determines the indices of the principal congruence subgroups of the Bianchi groups $B_d$, $SL(2,\mathcal O)$ and elementary matrix group $E$ and extends Wohlfahrt's Theorem to $B_d$, $SL(2,\mathcal O)$ and $E$, where $\mathcal O$ is the ring of integers of some number fields.

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