Overview

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: Actions, Commutator Identities, and Algebraic Eraser (I Anshel et al.) Virtually Free-By-Cyclic One-Relator Groups: I (G Baumslag & D Troger) Some Cryptoprimitives for Noncommutative Algebraic Cryptography (G Baumslag et al.) On the Derived Subgroups of the Free Nilpotent Groups of Finite Rank (R D Blyth et al.) A Recurrence Relation for the Number of Free Subgroups in Free Products of Cyclic Groups (T Camps et al.) The Baumslag-Solitar Groups: A Solution for the Isomorphism Problem (A E Clement) Unification Theorems in Algebraic Geometry (E Daniyarova et al.) Reflections of Commutative Transitivity (B Fine & G Rosenberger) Groups Universally Equivalent to Free Burnside Groups of Prime Exponent and a Question of Philip Hall (A Gaglione et al.) Changing Generators in Nonfree Groups (R Goldstein) Matrix Completions Over Principal Ideal Rings (W H Gustafson et al.) A Primer on Computational Group Homology and Cohomology (D Joyner) Doubles of Residually Solvable Groups (D Kahrobaei) An Application of a Group of Ol'shanskii to a Question of Fine et al. (S Lipschutz & D Spellman) Quotient Isomorphism Invariants of a Finitely Generated Coxeter Group (M Mihalik et al.) Localization and I A -automorphisms of Finitely Generated, Metabelian, and Torsion-Free Nilpotent Groups (M Zyman) Readership: Graduate students and researchers in mathematics.

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