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arXiv:math/0509024 [math.GR]AbstractReferencesReviewsResources

Growth and generation in SL_2(Z/pZ)

H. A. Helfgott

Published 2005-09-01, updated 2008-01-08Version 4

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.

Comments: 21 pages; fourth version - lemmas on escape amended and improved; to appear in Annals of Mathematics
Categories: math.GR, math.CO, math.NT
Subjects: 05C25, 20G40, 20D60, 11B75
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