In mathematics, an Igusa group or Igusa subgroup is a subgroup of the Siegel modular group defined by some congruence conditions. They were introduced by .
The symplectic group Sp<sub>2g</sub>(Z) consists of the matrices
such that AB<sup>t</sup> and CD<sup>t</sup> are symmetric, and AD<sup>t</sup> â CB<sup>t</sup> = I (the identity matrix).
The Igusa group ÃÂ<sub>g</sub>(n,2n) = ÃÂ<sub>n,2n</sub> consists of the matrices
in Sp<sub>2g</sub>(Z) such that B and C are congruent to 0 mod n, A and D are congruent to the identity matrix I mod n, and the diagonals of AB<sup>t</sup> and CD<sup>t</sup> are congruent to 0 mod 2n. We have ÃÂ<sub>g</sub>(2n) â ÃÂ<sub>g</sub>(n,2n) â ÃÂ<sub>g</sub>(n) where ÃÂ<sub>g</sub>(n) is the subgroup of matrices congruent to the identity modulo n.