**Contemporary Mathematics**

Volume: 421;
2007;
273 pp;
Softcover

MSC: Primary 01; 03; 20;

Print ISBN: 978-0-8218-3985-0

Product Code: CONM/421

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

**Electronic ISBN: 978-0-8218-8100-2
Product Code: CONM/421.E**

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

# Combinatorial Group Theory, Discrete Groups, and Number Theory

Share this page *Edited by *
*Benjamin Fine; Anthony M. Gaglione; Dennis Spellman*

This volume consists of contributions by participants and speakers at two conferences. The first was entitled Combinatorial Group Theory, Discrete Groups and Number Theory and was held at Fairfield University, December 8–9, 2004. It was in honor of Professor Gerhard Rosenberger's sixtieth birthday. The second was the AMS Special Session on Infinite Group Theory held at Bard College, October 8–9, 2005. The papers in this volume provide a very interesting mix of combinatorial group theory, discrete group theory and ring theory as well as contributions to noncommutative algebraic cryptography.

#### Readership

Graduate students and research mathematicians interested in group theory.

# Table of Contents

## Combinatorial Group Theory, Discrete Groups, and Number Theory

- Contents iii4 free
- A Description of the Arithmetic Fuchsian Groups with Signature (2; -) 18 free
- Outer Automorphism Groups of Certain Orientable Seifert 3-Manifold Groups 1522
- The Search for Origins of the Commutator Calculus 2330
- A Note on Nondiscrimination of Nilpotent Groups and Mal'cev Completions 2936
- A Proposed Public Key Cryptosystem Using the Modular Group 3542
- Gröbner Basis Techniques in the Computation of Two-Sided Syzygies 4552
- Normal Subgroups of the Modular Group and Other Hecke Groups 6572
- Commutativity of Units in Group Rings 8794
- Presentations of Groups Involving More Generators Than Are Necessary. II. 101108
- Unions of Varieties and Quasivarieties 113120
- Finitely Presented Infinite Torsion Groups and a Question of V. H. Dyson 119126
- Context-Free Irreducible Word Problems in Groups 125132
- Autocommutators and the Autocommutator Subgroup 137144
- Informative Words and Discreteness 147154
- An Algorithm for Potentially Positive Words in F2 157164
- Using Group Theory for Knowledge Representation and Discovery 169176
- Quotient Tests and Gröbner Bases 187194
- 0. Introduction 187194
- 1. The Word Problem in Groups 188195
- 2. Quotient Tests 189196
- 3. Linear Representations of Groups 189196
- 4. Universal Linear Representations 191198
- 5. Linear Quotient Tests and Gröbner Basis Techniques 192199
- 6. Some Examples 195202
- 7. Classification of Finite Generalized Triangle and Tetrahedron Groups 196203
- References 200207

- Transitivity of Normality and Pronormal Subgroups 201208
- Torsion in Maximal Arithmetic Fuchsian Groups 213220
- Nilpotent Q[x]-Powered Groups 227234
- On the Rosenberger Monster 251258
- Density of Test Elements in Finite Abelian Groups 261268
- Adjoining a Root Does Not Decrease the Rank 269276