Growth of small generating sets in SL_n(Z/pZ)
Group Theory
2010-09-13 v2 Combinatorics
Number Theory
Abstract
Let G=SL_n. Let K=Z/pZ, p a prime. Let A\subset G(K) generate G(K). Suppose that |A|<p^{n+1-\delta}, delta>0. Then |A A A|>>|A|^{1+\epsilon}, where epsilon>0 and the implied constant depend only on n and delta.
Cite
@article{arxiv.1002.1605,
title = {Growth of small generating sets in SL_n(Z/pZ)},
author = {Nick Gill and Harald Andres Helfgott},
journal= {arXiv preprint arXiv:1002.1605},
year = {2010}
}
Comments
19 pages; typos removed, some proofs shortened