Generation of Finite Groups

Erscheinungsjahr 2027
ISBN: 978-3-032-33738-2
Verlag: Birkhäuser

Buch, Englisch, 222 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Frontiers in Mathematics

This book collects results obtained over two decades on the generation of finite groups, a central topic in group theory. Since these results strongly depend on the classification of simple groups, a preliminary chapter with all the necessary information about simple groups to address the various generation problems is included.

Presenting both classical results and recent advancements in the field, the book bridges the gap between introductory texts and specialized research papers.

With each chapter featuring carefully selected exercises, this comprehensive and cohesive resource aims at being an accessible volume that could, for example, also appeal to a student who has taken an introductory course in group theory.

Zielgruppe

Research

Autoren/Hrsg.

Lucchini, Andrea

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Chapter 1. Simple and almost simple groups.- Chapter 2. Generators and normal subgroups.- Chapter 3. Generation and conditional probability.- Chapter 4. Monolithic groups with abelian socle.- Chapter 5. Monolithic groups with nonabelian socle.- Chapter 6. Crowns.- Chapter 7. Using crowns in the computation of d(G) and PG(d).- Chapter 8. Applications.- Chapter 9. Permutation groups.- Chapter 10. A computational approach to the minimum generating set problem.- Chapter 11. The expected number of random elements to generate a finite group.- Chapter 12. Minimal generating sets of different sizes.- Chapter 13. Generating sets containing a prescribed subset.- Chapter 14. The presentation rank.- Chapter 15. Graphs encoding the generating properties of a finite group.

Über Autor(innen)

Andrea Lucchini received his PhD in Mathematics in 1990 and has been a full professor at the University of Padova since 2007, having previously held a position at the University of Brescia. He has served as the scientific coordinator of several research projects on group theory and its applications and from 2019 to 2024, he was the Coordinator of the Natural Sciences branch of the prestigious Galilean School for Higher Education. He is a member of the editorial boards of the Journal of Group Theory and the Rendiconti del Seminario Matematico dell'Università di Padova. An author of more than 200 papers in group theory, his research focuses on the minimum number of generators of finite groups, probabilistic methods in group theory, invariable generation, the probabilistic zeta function of profinite groups, and the generating graph of finite groups — precisely the themes developed in this book.