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math.GR2010★ 24 cited
Growth in solvable subgroups of GL_r(Z/pZ)
Nick Gill, Harald Andres Helfgott
Let and let be a subset of $\GL_r(K)$ such that is solvable. We reduce the study of the growth of under the group operation to the nilpotent setting. Specifi…
math.GR2010
Growth of small generating sets in SL_n(Z/pZ)
Nick Gill, Harald Andres Helfgott
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-δ}, delta>0. Then |A A A|>>|A|^{1+ε}, where epsilon>0 and the implied constant depend on…