Linear Groups and Computation

Auteur

Dane Flannery, PhD, is a Senior Lecturer in Mathematics at the National University of Ireland, Galway.

Alla Detinko, PhD, is a Research Fellow at the National University of Ireland, Galway.

Résumé

This book covers computational group theory (CGT), an active, rapidly expanding field at the interface of mathematics and computer science. It is the first systematic effort to establish computing with infinite matrix groups on the same footing as the rest of CGT. The book emphasizes practical methods based on results of linear group theory, solutions of fundamental algorithmic problems, and provision of software. Additionally, the book sets out a research program to make further progress in the area.

Contenu

Part I. Basic Concepts and Constructions. The Elements of Linear Group Theory. Classes of Linear Groups. Finitely Generated Linear Groups. Part II. Computing with Finitely Generated Matrix Groups. Finiteness. The Tits Alternative and Related Problems. Computing in Linear Groups of Finite Rank.