Growth in SL3(Z/pZ)
نویسنده
چکیده
Let G = SL3(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| for some ǫ > 0. Then |A ·A ·A| > |A| , where δ > 0 depends only on ǫ. We will also study subsets A ⊂ G that do not generate G. Other results on growth and generation follow.
منابع مشابه
Growth and generation in SL2(Z/pZ
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)) elements of A ∪ A, where c and the implied constant are absolute.
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