On the ergodicity of difference distribution tables of random permutations

Properties of the Markov chain induced by the difference distribution table of a random permutation acting on a finite group $G$ are considered. The ergodicity probability and the convergence rate of this Markov chain are estimated. It is proved that the group generated by permutations $x\mapsto s(xa)$, $x,a\in G$, is $2$-transitive for almost all permutations $s$ from the permutation group of $G$.