Growth and generation in SL_2(Z/pZ)
Group Theory
2008-01-08 v4 Combinatorics
Number Theory
Abstract
We show that every subset of SL_2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL_2(Z/pZ), every element of SL_2(Z/pZ) can be expressed as a product of at most O((log p)^c) elements of the union of A and A^{-1}, where c and the implied constant are absolute.
Cite
@article{arxiv.math/0509024,
title = {Growth and generation in SL_2(Z/pZ)},
author = {H. A. Helfgott},
journal= {arXiv preprint arXiv:math/0509024},
year = {2008}
}
Comments
21 pages; fourth version - lemmas on escape amended and improved; to appear in Annals of Mathematics