Here are some terms that are non-trivial.
- Congruence Subgroup
- Any subgroup of the modular group which contains some principal congruence subgroup.
- Elliptic (of matrices)
- A Möbius transformation whose fixed points are exactly two distinct complex conjugate points.
- Modular Group
- The set of 2×2 matrices with integer entries and determinant 1. In many applications elements of the modular group are identified with their negatives and/or determinants of -1 are allowed as well.
- Principal Congruence Subgroup of Level m
- The subgroup of the modular group whose elements are all congruent to the identity modulus some natural number n. Note that the principal congruence subgroup of level 1 is the entire modular group.