Computation of orders and cycle lengths of automorphisms of finite solvable groups

2017/07/07 by Bors, Alexander
#12E20 #15A21 #20D45. Secondary: 12E05 #FOS: Mathematics #Group Theory (math.GR) #Primary: 20D10

paper · doi:10.48550/arxiv.1707.02368

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.

Related

• Finite groups with an automorphism of large order
• On finite groups where the order of every automorphism is a cycle length
• Towards the Automorphism Conjecture I: Combinatorial Control
• Cycle lengths in finite groups and the size of the solvable radical
• Classification of finite group automorphisms with a large cycle