Complex sentence: The functional equation, i.e., the behavior of "f" with respect to can be relaxed by requiring it only for matrices in smaller groups, such as a subgroup "G" of of SL (2, Z) that is of finite index.
Split into simpler sentences: The functional equation, i.e., the behavior of "f" with respect to can be relaxed by requiring it only for matrices in smaller groups. Let "G" be a subgroup of SL (2, Z) that is of finite index.