The minimal faithful permutation degree of groups without Abelian normal subgroups

The minimal faithful permutation degree 𝜇⁡(𝐺) of a finite group 𝐺 is the smallest integer 𝑚 for which there is an injective homomorphism 𝜙 from 𝐺 to 𝑆𝑚. The main result of this paper is a randomized polynomial-time algorithm for computing the minimal faithful permutation degree groups without abelian normal subgroups. Additionally, we show that: 1. For any primitive permutation group 𝐺, 𝜇⁡(𝐺) can be computed in quasi-polynomial time. 2. For a group 𝐺 given by its Cayley table, 𝜇⁡(𝐺) can be computed in DSPACE⁡(log3⁡|𝐺|).