On Large Orbits of Actions of Finite Soluble Groups: Applications

The Chebotarev invariant of a finite group: A conjecture of Kowalski and Zywina

“…for some absolute constants c 1 and c 2 and notice that there exists c 3 such that if k ≥ c 3 (log |G|) 2 , then the right-hand tends to zero as |G| → ∞.…”