Some semigroup or monoid presentations

ABSTRACT MSc THESIS SOME SEMIGROUP AND MONOID PRESENTATIONS DEFINING A GROUP BASRİ ÇALIŞKAN DEPARTMENT OF MATHEMATICS INSTITUTE OF NATURAL AND APPLIED SCIENCES UNIVERSITY OF ÇUKUROVA Supervisor : Assoc.Prof.Dr. Fikret KUYUCU Year: 2002, Pages:64 Jury : Assoc.Prof.Dr. Fikret KUYUCU : Assoc.Prof.Dr. Hayrullah AYIK : Assoc.Prof.Dr. Hüseyin BİLGİÇ Semigroup presentations have been studied for a long time. In 1990, E. F. Robertson and Y. Ünlü wrote a computer program for semigroups similar to the Todd- Coxeter algorithm for groups. After 1990, this subject has been worked extensively and many works have been published in this area. There are two methods in combinatorial semigroup theory. First, to find the semigroup defined by a given presentation. Second, to find the presentation representing a given semigroup. In this thesis, we applied the first. Since every group is a semigroup, we can consider either the semigroup or monoid presentation of a group G as the group presentation of G. We also searched whether semigroup or monoid presentations define a group. Some of these presentations have either two generators and one relation or two generators and two relations. It appeared that some of them are well-known groups in the literature. Key Words: Semigroup, Monoid, Presentation, Rewriting Systems, Knuth-Bendix Procedure. II