Book contents
- Frontmatter
- Contents
- Introduction
- 1 Finite group schemes
- 2 Algorithms for polycyclic groups
- 3 The spread of finite and infinite groups
- 4 Discrete subgroups of semisimple Lie groups, beyond lattices
- 5 Complete reducibility and subgroups of exceptional algebraic groups
- 6 Axial algebras of Jordan and Monster type
- 7 An introduction to the local-to-global behaviour of groups acting on trees and the theory of local action diagrams
- 8 Finite groups and the class-size prime graph revisited
- 9 Character bounds for finite simple groups and applications
- 10 Generalized Baumslag-Solitar groups: a topological approach
- References
2 - Algorithms for polycyclic groups
Published online by Cambridge University Press: 21 November 2024
Book contents
- Frontmatter
- Contents
- Introduction
- 1 Finite group schemes
- 2 Algorithms for polycyclic groups
- 3 The spread of finite and infinite groups
- 4 Discrete subgroups of semisimple Lie groups, beyond lattices
- 5 Complete reducibility and subgroups of exceptional algebraic groups
- 6 Axial algebras of Jordan and Monster type
- 7 An introduction to the local-to-global behaviour of groups acting on trees and the theory of local action diagrams
- 8 Finite groups and the class-size prime graph revisited
- 9 Character bounds for finite simple groups and applications
- 10 Generalized Baumslag-Solitar groups: a topological approach
- References
Summary
This paper gives a survey about the currently used methods for computing with polycyclic groups. It discusses the different representations for polycyclic groups, gives a brief outline of many existing methods and considers two algorithms in a little more detail: the Frattini subgroup algorithm and the methods for solving the conjugacy problem. The final section of the paper exhibits some open problems.
- Type
- Chapter
- Information
- Groups St Andrews 2022 in Newcastle , pp. 53 - 73Publisher: Cambridge University PressPrint publication year: 2024
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