Product decompositions of quasirandom groups and a Jordan type theorem

Details Product decompositions of quasirandom groups and a Jordan type theorem Product decompositions of quasirandom groups and a Jordan type theorem

2007-03-12

arxiv.org/abs/math/0703343v3

Mathematics

Group Theory

18 pages. In this third version we added an Appendix with a short proof of Proposition 0

Scientific paper

We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If k is the minimal degree of a representation of the finite group G, then for every subset B of G with $|B| > |G| / k^{1/3}$ we have B^3 = G. We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan's theorem which implies that if k>1, then G has a proper subgroup of index at most ck^2 for some absolute constant c, hence a product-free subset of size at least $|G| / c'k$. This answers a question of Gowers.

Affiliated with

Also associated with

No associations

Rating

Product decompositions of quasirandom groups and a Jordan type theorem 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 Product decompositions of quasirandom groups and a Jordan type theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Product decompositions of quasirandom groups and a Jordan type theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-285992