Bianchi group

In mathematics, a Bianchi group is a group of the form

where d is a positive square-free integer. Here, PSL denotes the projective special linear group and ${\displaystyle {\mathcal {O}}_{d}}$ is the ring of integers of the imaginary quadratic field ${\displaystyle \mathbb {Q} ({\sqrt {-d}})}$.

The groups were first studied by Bianchi (1892) as a natural class of discrete subgroups of ${\displaystyle PSL_{2}(\mathbb {C} )}$, now termed Kleinian groups.

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