Inequalities for finite group permutation modules

Details Inequalities for finite group permutation modules Inequalities for finite group permutation modules

2003-10-11

arxiv.org/abs/math/0310169v1

Mathematics

Group Theory

27 pages

Scientific paper

If f is a nonzero complex-valued function defined on a finite abelian group A and \hat f is its Fourier transform, then |Supp (f)||Supp {\hat f)| \ge |A|, where Supp (f) and Supp (\hat f) are the supports of f and \hat f. In this paper we generalize this known result in several directions. In particular, we prove an analogous inequality where the abelian group A is replaced by a transitive right G-set, where G is an arbitrary finite group. We obtain stronger inequalities when the G-set is primitive and we determine the primitive groups for which equality holds. We also explore connections between inequalities of this type and a result of Chebotar\"ev on complex roots of unity, and we thereby obtain a new proof of Chebotar\"ev's theorem.

Affiliated with

Also associated with

No associations

Rating

Inequalities for finite group permutation modules 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 Inequalities for finite group permutation modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inequalities for finite group permutation modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-229720