Profinite groups, profinite completions and a conjecture of Moore

Mathematics – Group Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

14 pages, LATeX

Scientific paper

Let R be any ring (with 1), \Gamma a group and R\Gamma the corresponding group ring. Let H be a subgroup of \Gamma of finite index. Let M be an R\Gamma -module, whose restriction to RH is projective. Moore's conjecture: Assume for every nontrivial element x in \Gamma, at least one of the following two conditions holds: M1) the subgroup generated by x intersects H non-trivially (in particular this holds if \Gamma is torsion free). M2) ord(x) is finite and invertible in R. Then M is projective as an R\Gamma-module. More generally, the conjecture has been formulated for crossed products R*\Gamma and even for strongly graded rings R(\Gamma). We prove the conjecture for new families of groups, in particular for groups whose profinite completion is torsion free. The conjecture can be formulated for profinite modules M over complete groups rings [[R\Gamma ]] where R is a profinite ring and \Gamma a profinite group. We prove the conjecture for arbitrary profinite groups. This implies Serre's theorem on cohomological dimension of profinite groups.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Profinite groups, profinite completions and a conjecture of Moore does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Profinite groups, profinite completions and a conjecture of Moore, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Profinite groups, profinite completions and a conjecture of Moore will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-536691

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.