Growth and generation in SL2(Z/pZ)
Abstract
We show that every subset of SL2(Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL2(Z/pZ), every element of SL2(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.
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