**Contemporary Mathematics**

Volume: 511;
2010;
200 pp;
Softcover

MSC: Primary 20; 17; 18;

Print ISBN: 978-0-8218-4805-0

Product Code: CONM/511

List Price: $73.00

Individual Member Price: $58.40

**Electronic ISBN: 978-0-8218-8190-3
Product Code: CONM/511.E**

List Price: $73.00

Individual Member Price: $58.40

# Computational Group Theory and the Theory of Groups, II

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

This volume consists of contributions by researchers who were invited to the Harlaxton Conference on Computational Group Theory and Cohomology, held in August of 2008, and to the AMS Special Session on Computational Group Theory, held in October 2008.

This volume showcases examples of how Computational Group Theory can be applied to a wide range of theoretical aspects of group theory. Among the problems studied in this book are classification of \(p\)-groups, covers of Lie groups, resolutions of Bieberbach groups, and the study of the lower central series of free groups. This volume also includes expository articles on the probabilistic zeta function of a group and on enumerating subgroups of symmetric groups.

Researchers and graduate students working in all areas of Group Theory will find many examples of how Computational Group Theory helps at various stages of the research process, from developing conjectures through the verification stage. These examples will suggest to the mathematician ways to incorporate Computational Group Theory into their own research endeavors.

#### Table of Contents

# Table of Contents

## Computational Group Theory and the Theory of Groups, II

- Contents v6 free
- Preface vii8 free
- The probabilistic zeta function 110 free
- Periodicities for graphs of p-groups beyond coclass 1120
- Computing covers of Lie algebras 2534
- Enumerating subgroups of the symmetric group 3342
- Weight five basic commutators as relators 3948
- 1. Introduction 4049
- 2. Preliminary results 4251
- 3. Rank 3 4655
- 4. Rank 4 6574
- 5. Rank 5 and greater 7584
- Appendix A. A list of critical commutators in rank 3 7887
- Appendix B. Some important weight six basic commutators 7988
- Appendix C. Some important transformations of nonbasic commutators 8089
- References 8190

- Basic commutators as relations: A computational perspective 8392
- Groups of minimal order which are not n-power closed 93102
- On the covering number of small alternating groups 109118
- Certain homological functors of 2-generator p-groups of class 2 127136
- Geometric algorithms for resolutions for Bieberbach groups 167176
- Nonabelian tensor product of soluble minimax groups 179188
- Finite groups have short rewriting systems 185194

#### Readership

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