Let be a natural number. Write
for the projection from the special linear group induced by the quotient projection to the integers modulo n.
The mod- congruence subgroups of the special linear group (essentially the modular group) are the preimages under of subgroups of .
Some of these have traditional names and symbols;
The principal congruence subgroup is the preimage of the trivial group:
This is the origin of the term: the elements of are congruent modulo to the identity.
The other two congruence subgroups having special symbols are
See at level structure – relation to spin structure.
A list of congruence subgroups is provided in
Last revised on December 8, 2022 at 23:18:42. See the history of this page for a list of all contributions to it.