In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple...

Ramanujan's congruences, congruences for the partition function, p(n), first discovered by Ramanujan in 1919 Congruence subgroup, a subgroup defined by...

0, or 1, so these subgroups are torsion-free groups. (There are other torsion-free subgroups.) The principal congruence subgroup of level 2, Γ(2), is...

integer. These are always finite-index subgroups and the congruence subgroup problem roughly asks whether all subgroups are obtained in this way. The conjecture...

In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...

( N ) {\displaystyle \Gamma (N)} principal congruence subgroup of level N {\displaystyle N} . A subgroup Γ ⊆ S L 2 ( Z ) {\displaystyle \Gamma \subseteq...

)}  ; they belong to a more general class of finite-index subgroups, congruence subgroups. Any order in a quaternion algebra over Q {\displaystyle \mathbb...

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...

the ring of modular forms M(Γ) is finitely generated when Γ is a congruence subgroup of SL(2, Z). In 2003, Lev Borisov and Paul Gunnells showed that the...

a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term...