Strange images of profinite groups

Abstract

We investigate whether a finitely generated profinite group G could have a finitely generated infinite image. A result of Dan Segal shows that this is impossible if G is prosoluble. We prove that such an image does not exist if G is semisimple or nonuniversal. We also investigate the existense of dense normal subgroups in $G$.Comment: The results of this preprint have been superceded by http://arxiv.org/abs/1102.3037 which answers the questions posed her