Congruence subgroup

A congruence subgroup of

S L_{n} (Z)

contains the kernel of reduction modulo some positive integer.

Table of contents
- Principal congruence subgroup Congruence subgroup

Principal congruence subgroup ( $Γ (N)$ )

The principal congruence subgroup of level

N

is

Γ (N) = ker (S L_{n} (Z) ⟶ S L_{n} (Z / N Z)) .

It has finite index because the target is finite.

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