LetKbe an algebraic function field with field of constantskand leiCbe the intersection of all but one of the valuation rings which determine the places ofK. This paper is concerned with the Serre groupsGL2(C). (Serre devotes much of his book “Trees” to their study.) Whenkis finiteCis an arithmetic Dedekind domain and (consequently) most of the work in this case has centred on the congruence subgroups. The purpose of this paper is to extend some of these results to the infinite case. Whenkis infinite it is proved, in particular, that, for infinitely manyC-idealsq, the principal congruence subgroupSL2(C, q), modulo its subgroup generated by unipotent matrices, has a free quotient of infinite rank. This result is used to extend known results on congruence hulls.