Poly-log Diameter Bounds for Some Families of Finite Groups

  title={Poly-log Diameter Bounds for Some Families of Finite Groups},
  author={OREN DINAI},
  • Published 2004
Fix a prime p and an integer m with p > m ≥ 2. Define the family of finite groups Gn := SLm (Z/p n Z) for n = 1, 2, . . .. We will prove that there exist two positive constants C and d such that for any n and any generating set S ⊆ Gn, diam(Gn, S) ≤ C · log(|Gn|) when diam (G, S) is the diameter of the finite group G with respect to the set of generators S. It is defined as the maximum over g ∈ G of the length of the shortest word in S ∪ S−1 representing g. This result shows that these families… CONTINUE READING

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