6,787 research outputs found
Strong approximation methods in group theory, an LMS/EPSRC Short course lecture notes
These are the lecture notes for the LMS/EPSRC short course on strong
approximation methods in linear groups organized by Dan Segal in Oxford in
September 2007.Comment: v4: Corollary 6.2 corrected, added a few small remark
Strange images of profinite groups
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normal subgroups in .Comment: The results of this preprint have been superceded by
http://arxiv.org/abs/1102.3037 which answers the questions posed her
Algebraic properties of profinite groups
Recently there has been a lot of research and progress in profinite groups.
We survey some of the new results and discuss open problems. A central theme is
decompositions of finite groups into bounded products of subsets of various
kinds which give rise to algebraic properties of topological groups.Comment: This version has some references update
- …