Algorithmic Problems in Groups and Semigroups

1. Front Matter

   Pages i-x

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2. Syntactic and Global Semigroup Theory: A Synthesis Approach

   • Jorge Almeida, Benjamin Steinberg

   Pages 1-23

3. Semigroups with Central Idempotents

   • Karl Auinger

   Pages 25-33

4. Algebraic Geometry over Groups

   • Gilbert Baumslag, Alexei Myasnikov, Vladimir Remeslennikov

   Pages 35-50

5. Aspects of the Theory of Free Groups

   • Katalin Bencsath, Benjamin Fine, Anthony M. Gaglione, Alexei G. Myasnikov, Frank Roehl, Gerhard Rosenberger et al.

   Pages 51-90

6. Polynomial Isoperimetric Inequalities for Richard Thompson’s Groups F, T, and V

   • V. S. Guba

   Pages 91-120

7. Ordered Monoids and J-Trivial Monoids

   • Karsten Henckell, Jean-Eric Pin

   Pages 121-137

8. A Remark on Finitely Generated Subgroups of Free Groups

   • S. V. Ivanov, P. E. Schupp

   Pages 139-142

9. Homotopy Reduction Systems for Monoid Presentations II: The Guba—Sapir Reduction and Homotopy Modules

   • Yuji Kobayashi

   Pages 143-159

10. Algorithmic Problems for Finite Groups and Finite Semigroups

    • S. I. Kublanovskii

    Pages 161-170

11. A Survey on the Computational Power of Some Classes of Finite Monoid Presentations

    • Friedrich Otto

    Pages 171-194

12. Rewriting Systems, Finiteness Conditions, and Associated Functions

    • S. J. Pride, Jing Wang

    Pages 195-216

13. Multiparty Communication Complexity of Finite Monoids

    • Jean-François Raymond, Pascal Tesson, Denis Thérien

    Pages 217-233

14. Presentations for Monoids, Their Maximal Subgroups, and Schützenberger Groups

    • N. Ruškuc

    Pages 235-249

15. On the Growth of Relatively Free Semigroups

    • L. M. Shneerson

    Pages 251-265

16. When Can One Finite Monoid Simulate Another

    • Howard Straubing

    Pages 267-288

17. Computing Closures of Finitely Generated Subgroups of the Free Group

    • Pascal Weil

    Pages 289-307

18. Back Matter

    Pages 309-309

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This volume contains papers which are based primarily on talks given at an inter­ national conference on Algorithmic Problems in Groups and Semigroups held at the University of Nebraska-Lincoln from May ll-May 16, 1998. The conference coincided with the Centennial Celebration of the Department of Mathematics and Statistics at the University of Nebraska-Lincoln on the occasion of the one hun­ dredth anniversary of the granting of the first Ph.D. by the department. Funding was provided by the US National Science Foundation, the Department of Math­ ematics and Statistics, and the College of Arts and Sciences at the University of Nebraska-Lincoln, through the College's focus program in Discrete, Experimental and Applied Mathematics. The purpose of the conference was to bring together researchers with interests in algorithmic problems in group theory, semigroup theory and computer science. A particularly useful feature of this conference was that it provided a framework for exchange of ideas between the research communities in semigroup theory and group theory, and several of the papers collected here reflect this interac­ tion of ideas. The papers collected in this volume represent a cross section of some of the results and ideas that were discussed in the conference. They reflect a synthesis of overlapping ideas and techniques stimulated by problems concerning finite monoids, finitely presented mono ids, finitely presented groups and free groups.

• Group theory
• complexity
• geometry
• groups
• semigroups-algorithmic theory
• statistics
• theoretical computer science logic
• algorithm analysis and problem complexity
• combinatorics

• Faculty of Computer Science, Dalhousie University, Halifax, Canada

  Jean-Camille Birget

• Dept. of Mathematics & Computer Science, Bar-Ilan University, Ramat Gan, Israel

  Stuart Margolis

• Dept. of Mathematics & Statistics, University of Nebraska, Lincoln, USA

  John Meakin

• Dept. of Mathematics, Vanderbilt University, Nashville, USA

  Mark Sapir

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