Groups with infinite mod-p Schur multiplier

The non-finiteness of the mod-p Schur multiplier of a finitely generated group G with trivial center implies the existence of uncountably many non-residually finite, non-isomorphic central extension groups with kernel C_p (see Thm. A). This phenomenon is related to the comparison of the cohomology of the profinite completion Gˆ of a group G and the cohomology of the group G itself (see Thm. B); according to J-P. Serre [8] a group G is good if the cohomologies of Gˆ and G are naturally isomorphic on finite coefficients. It is shown that non-uniform arithmetic lattices of algebraic rank 1 groups over local fields of positive characteristic p are not good (see Thm. C).