Computational Group Theory and the Theory of Groups

by Kappe, Luise-charlotte; Magidin, Arturo; Morse, Robert Fitzgerald

• ISBN13: 9780821843659
• ISBN10: 0821843656
• Format: Paperback
• Copyright: 2008-11-02
• Publisher: Amer Mathematical Society

Summary

"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."--BOOK JACKET.

Table of Contents

On the application of computational group theory to the theory of groups

A classification of certain maximal subgroups of alternating groups

On the nonabelian tensor squares of free nilpotent groups of finite rank

Investigating $p$-groups by coclass with GAP

Homological algebra programming

Groups with a finite covering by isomorphic abelian subgroups

On some subnormality conditions in metabelian groups

Normalizer calculation using automorphisms

Group theory in SAGE

Simultaneous constructions of the sporadic groups $\mathsf{Co_2}$ and $\mathsf{Fi_{22}}$

Constructing simple groups from irreducible subgroups of $GL_n(2)$

Dickson polynomials and the norm map between the Hecke algebras of Gelfand-Graev representations

On orbit equivalent, two-step imprimitive permutation groups

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