Growth in finite simple groups of Lie type

Details Growth in finite simple groups of Lie type Growth in finite simple groups of Lie type

2010-01-25

arxiv.org/abs/1001.4556v1

Mathematics

Group Theory

Research announcement

Scientific paper

We prove that if L is a finite simple group of Lie type and A a symmetric set of generators of L, then A grows i.e |AAA| > |A|^(1+epsilon) where epsilon depends only on the Lie rank of L, or AAA=L. This implies that for a family of simple groups L of Lie type the diameter of any Cayley graph is polylogarithmic in |L|. Combining our result on growth with known results of Bourgain,Gamburd and Varj\'u it follows that if LAMBDA is a Zariski-dense subgroup of SL(d,Z) generated by a finite symmetric set S, then for square-free moduli m which are relatively prime to some number m_0 the Cayley graphs Gamma(SL(d,m),pi_m(S)) form an expander family.

Affiliated with

Also associated with

No associations

Rating

Growth in finite simple groups of Lie type 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 Growth in finite simple groups of Lie type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Growth in finite simple groups of Lie type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643580