Aspects of infinite groups : a festschrift in honor of Anthony Gaglione / editors Benjamin Fine, Gerhard Rosenberger, Dennis Spellman.

Format:

Book

Contributor:

Gaglione, Anthony M.

Fine, Benjamin, 1948-

Rosenberger, Gerhard.

Spellman, Dennis, 1945-

Series:

Algebra and discrete mathematics (World Scientific (Firm)) ; v. 1.

Algebra and discrete mathematics, 1793-5873 ; v. 1

Language:

English

Subjects (All):

Infinite groups.

Representations of groups.

Physical Description:

1 online resource (253 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, N.J. : World Scientific, c2008.

Language Note:

English

Summary:

This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.

Contents:

6. Formal Power Series Rings and the Magnus Representation7. Relations on the Variables; 8. References; On the Derived Subgroups of the Free Nilpotent Groups of Finite Rank R. D. Blyth, P. Moravec and R. F. Morse; 1. Introduction; 2. The Derived Subgroup of a Free Nilpotent Group; 3. Application; Acknowledgements; References; A Recurrence Relation for the Number of Free Subgroups in Free Products of Cyclic Groups T. Camps, M. Darfer and G. Rosenberger; 1. Introduction; 2. Preliminaries; 3. The Main Results; 4. Examples; References

The Baumslag-Solitar Groups: A Solution for the Isomorphism Problem A. E. Clement1. Introduction; 2. Notation; 3. The proof of Theorem 1.1; Acknowledgments; References; Unification Theorems in Algebraic Geometry E. Daniyarova, A. Myasnikov and V. Remeslennikov; CONTENTS; 1. Introduction; 2. Preliminaries; 2.1. Languages and structures; 2.2. Theories; 3. Algebras; 3.1. Congruences; 3.2. Quasivarieties; 3.3. Universal closures; 3.4. A-Algebras; 4. Types, Zariski topology, and coordinate algebras; 4.1. Quantifier-free types and Zariski topology; 4.2. Coordinate algebras and complete types

4.3. Equationally Noetherian algebras5. Limit algebras; 5.1. Direct systems of formulas and limit algebras; 5.2. Limit A-algebras; 6. Unification Theorems; References; Reflections on Commutative Transitivity B. Fine and G. Rosenberger; 1. Introduction; 2. Commutative Transitivity and Commutative Transitive Groups; 3. Commutative Transitivity, CSA and Universally Free Groups; 4. The Commutative Transitive Kernel; 5. RG Groups and a Classification of One-Relator CT Groups; 6. Commutative Transitivity and Discriminating Groups; 7. An Extension of Commutative Thansitivity; 8. References

Groups Universally Equivalent to Free Burnside Groups of Prime Exponent and a Question of Philip Hall A. Gaglione, S. Lipschutz and D. Spellman

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

981-279-341-0

OCLC:

851970705