Linear Groups and Computation

1. Auflage 2027
ISBN: 978-1-041-54368-8
Verlag: Taylor & Francis

Buch, Englisch, 216 Seiten, Format (B × H): 178 mm x 254 mm

Linear Groups and Computation offers a comprehensive account of practical computation with finitely generated linear groups over infinite fields. Methodologies are developed to solve fundamental algorithmic problems, covering major classes of linear groups. Readers are introduced to a library of procedures designed for the computational recognition and structural investigation of these groups.

The book will appeal to researchers in algebra, its applications, and all areas of mathematics where linear groups are prominent. It is accessible to a broad audience, ranging from graduate students with basic algebraic prerequisites to experienced researchers.

Features:

- Self-contained and uniquely focused text, including all necessary background material

- Resource for advanced lecture courses and seminars, with exercises accompanying the chapters

- Numerous examples demonstrating the application of algorithms via computer experimentation

- Insights into emerging directions for future research.

Zielgruppe

Postgraduate

Autoren/Hrsg.

Detinko, Alla

Flannery, Dane

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Zahlensysteme
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Part 1: Linear groups 1. First principles 2. Classes of linear groups 3. Linear algebraic groups 4. Finitely generated linear groups Part 2: Computational finite approximation 5. Computing with finitely generated matrix groups 6. Finiteness testing 7. Deciding virtual solvability, and related problems 8. Computing in linear groups of finite rank Part 3: Zariski density and computing 9. From finite to strong approximation 10. Congruence subgroups and density 11. Algorithms for arithmetic groups 12. Experimenting with dense groups

Über Autor(innen)

Alla Detinko is a Senior Lecturer at the University of Huddersfield, UK. Having earned her PhD from the Academy of Sciences of Belarus, she served as an Associate Professor in Belarus until 2005, later holding research fellowships at the University of Galway, Ireland, and the University of St Andrews, UK. With decades of experience in group theory and its applications, Dr Detinko’s research focuses on linear groups and symbolic computation. Her work has been supported by major funding agencies such as Science Foundation Ireland and the European Commission (Horizon 2020 programme).

Dane Flannery is a Professor of Mathematics at the University of Galway, Ireland. After receiving a PhD from the Australian National University, he worked at universities in Australia as a postdoctoral fellow and lecturer before taking up a lectureship in Galway. His research encompasses linear group theory and combinatorial mathematics, with an emphasis on computational methods. He is the co-author, with Warwick de Launey, of Algebraic Design Theory (Mathematical Surveys and Monographs, American Mathematical Society).