Computation of orders and cycle lengths of automorphisms of finite solvable groups. (January 2022) - Bors, Alexander
Abstract: Let G be a finite solvable group, given through a refined consistent polycyclic presentation, and α an automorphism of G, given through its images of the generators of G . In this paper, we discuss algorithms for computing the order of α as well as the cycle length of a given element of G under α . We give correctness proofs and discuss the theoretical complexity of these algorithms. Along the way, we carry out detailed complexity analyses of several classical algorithms on finite polycyclic groups.