Computational Group Theory and the Theory of Groups
About this Title
Luise-Charlotte Kappe, Arturo Magidin and Robert Fitzgerald Morse, Editors
Publication: Contemporary Mathematics
Publication Year : Volume 470
ISBNs: 978-0-8218-4365-9 (print); 978-0-8218-8149-1 (online)
MathSciNet review: 2478409
The power of general purpose computational algebra systems running on personal computers has increased rapidly in recent years. For mathematicians doing research in group theory, this means a growing set of sophisticated computational tools are now available for their use in developing new theoretical results.
This volume consists of contributions by researchers invited to the AMS Special Session on Computational Group Theory held in March 2007. The main focus of the session was on the application of Computational Group Theory (CGT) to a wide range of theoretical aspects of group theory. The articles in this volume provide a variety of examples of how these computer systems helped to solve interesting theoretical problems within the discipline, such as constructions of finite simple groups, classification of $p$-groups via coclass, representation theory and constructions involving free nilpotent groups. The volume also includes an article by R. F. Morse highlighting applications of CGT in group theory and two survey articles.
Graduate students and researchers interested in various aspects of group theory will find many examples of Computational Group Theory helping research and will recognize it as yet another tool at their disposal.
Graduate students and research mathematicians interested in group theory and computational group theory.
Table of Contents
- Robert Fitzgerald Morse – On the application of computational group theory to the theory of groups [MR 2478410]
- Bret Benesh – A classification of certain maximal subgroups of alternating groups [MR 2478411]
- Russell D. Blyth, Primož Moravec and Robert Fitzgerald Morse – On the nonabelian tensor squares of free nilpotent groups of finite rank [MR 2478412]
- Heiko Dietrich, Bettina Eick and Dörte Feichtenschlager – Investigating -groups by coclass with GAP [MR 2478413]
- Graham Ellis – Homological algebra programming [MR 2478414]
- Tuval S. Foguel and Matthew F. Ragland – Groups with a finite covering by isomorphic abelian subgroups [MR 2478415]
- David Garrison and Luise-Charlotte Kappe – On some subnormality conditions in metabelian groups [MR 2478416]
- Alexander Hulpke – Normalizer calculation using automorphisms [MR 2478417]
- David Joyner and David Kohel – Group theory in SAGE [MR 2478418]
- Hyun Kyu Kim and Gerhard O. Michler – Simultaneous constructions of the sporadic groups and [MR 2478419]
- Gerhard O. Michler – Constructing simple groups from irreducible subgroups of [MR 2478420]
- Julianne G. Rainbolt – Dickson polynomials and the norm map between the Hecke algebras of Gelfand-Graev representations [MR 2478421]
- Ákos Seress and Keyan Yang – On orbit equivalent, two-step imprimitive permutation groups [MR 2478422]