  The Zorn's Algebra ZZ(R) has a multiplicative function called determinant
with properties similar to the usual one. The set of elements in ZZ(R) with
determinant 1 is a Moufang loop that we will denote by \GA. In our main result
we prove that if R is a Dedekind algebraic number domain that contains an
infinite order unit, each finite index subloop L, such that \GA has the weak
Lagrange property relative to L, is congruence subloop. In addition, if R=\Z,
then we present normal subloops of finite index in \GA that are not congruence
subloops.
