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

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...

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Bibliographic Details
Published inJournal of symbolic computation Vol. 108; pp. 117 - 136
Main Author Bors, Alexander
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.01.2022
Subjects
Computational group theory
Finite groups
Group automorphisms
Polycyclic groups
Polycyclic groups
Computational group theory
Finite groups
Group automorphisms
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Summary: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.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2020.04.004