# On the diameter of permutation groups

@article{Babai1992OnTD, title={On the diameter of permutation groups}, author={L. Babai and {\'A}kos Seress}, journal={Eur. J. Comb.}, year={1992}, volume={13}, pages={231-243} }

For a set S of generators of the finite group G, let diam(G, S) denote the maximum over g ∈ G of the minimal word length expressing g in terms of S ∪ S−1. We define the diameter of G as diam(G) = maxs diam(G, S) (‘worst case’ generators). For permutation groups G of degree n, we prove that diam(G) ≤ exp((n ln n)½(1 + o(1))). (This bound is asymptotically best possible.) For transitive permutation groups G of degree n, we obtain the bound diam(G) ≤ exp(c log3 n)diam(Ak), where Ak is the largest… CONTINUE READING

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