Computation of orders and cycle lengths of automorphisms of finite solvable groups. (January 2022)

• Record Type: Journal Article
• Authors: Bors, Alexander
• Is Part Of: Journal of symbolic computation. Volume 108(2022)
• Page Start: 117
• Page End: 136
• Publication Date: 2022-01
• Subjects: Finite groups -- Polycyclic groups -- Computational group theory -- Group automorphisms; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.04.004
• Languages: English
• ISSNs: 0747-7171

Abstract

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.