The Probability of Generating the Symmetric Group

Research paper by Stefan-Christoph Virchow

Indexed on: 08 Nov '16Published on: 08 Nov '16Published in: arXiv - Mathematics - Group Theory


We give a new proof of Dixon's conjecture: The probability that a pair of random permutations generates either $A_n$ or $S_n$ is $1-1/n+\mathcal {O}(n^{-\frac{3}{2}+\epsilon})$. Our proof is based on character theory and character estimates and does not need the classification of the finite simple groups.