H. A. Helfgott
Published 2008-07-14, updated 2009-06-08Version 3
Let G=SL_3(Z/pZ), p a prime. Let A be a set of generators of G. Then A grows under the group operation. To be precise: denote by |S| the number of elements of a finite set S. Assume |A| < |G|^{1-\epsilon} for some \epsilon>0. Then |A\cdot A\cdot A|>|A|^{1+\delta}, where \delta>0 depends only on \epsilon. We also study subsets A\subset G that do not generate G. Other results on growth and generation follow.
Comments: 88 pages; Theorem 1.1 is new
Growth and generation in SL_2(Z/pZ)
The $(2,3)$-generation of the finite simple orthogonal groups, I
The $(2,3)$-generation of the finite special unitary groups of dimension $n\geq 9$
![QR code for arXiv:0807.2027 [math.GR]](http://oss.arxitics.com/images/favicon.svg)