# Computational Group Theory and the Theory of Groups

Share this page *Edited by *
*Luise-Charlotte Kappe; Arturo Magidin; Robert Fitzgerald Morse*

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.

#### Readership

Graduate students and research mathematicians interested in group theory and computational group theory.

# Table of Contents

## Computational Group Theory and the Theory of Groups

- Contents v6 free
- Preface vii8 free
- On the application of computational group theory to the theory of groups 110 free
- A classification of certain maximal subgroups of alternating groups 2130
- Investigating p-groups by coclass with GAP 4554
- Homological algebra programming 6372
- Groups with a finite covering by isomorphic abelian subgroups 7584
- On some subnormality conditions in metabelian groups 8998
- Normalizer calculation using automorphisms 105114
- Group Theory in SAGE 115124
- Simultaneous constructions of the sporadic groups Co2 and Fi22 141150
- Constructing simple groups from irreducible subgroups of GLn(2) 235244
- Dickson polynomials and the norm map between the Hecke algebras of Gelfand-Graev representations 263272