Regular orbits in powers of permutation representations (Q5946707)

Let \((Q,G)\) be a faithful permutation representation of a finite group \(G\). Suppose the \(G\)-set \(Q\) has \(t\) distinct non-zero marks. The author of this paper proves that the direct power \((Q,G)^t\) of \((Q,G)\) contains a regular orbit. As a consequence, the probability that a random element of \(Q^r\) lies in a regular orbit of \((Q,G)^r\) tends to 1 exponentially fast as \(r\) tends to \(\infty\).