Semigroup presentations

[摘要] In this thesis we consider in detail the following two fundamental problems forsemigroup presentations:1. Given a semigroup find a presentation defining it.2. Given a presentation describe the semigroup defined by it.We also establish two links between these two approaches: semigroup constructionsand computational methods.After an introduction to semigroup presentations in Chapter 3, in Chapters 4and 5 we consider the first of the two approaches. The semigroups we examine inthese two chapters include completely O-simple semigroups, transformation semigroups,matrix semigroups and various endomorphism semigroups. In Chapter 6we find presentations for the following semi group constructions: wreath product,Bruck-Reilly extension, Schiitzenberger product, strong semilattices of monoids,Rees matrix semigroups, ideal extensions and subsemigroups. We investigate inmore detail presentations for subsemigroups in Chapters 7 and 10, where we provea number of Reidemeister-Schreier type results for semigroups. In Chapter 9we examine the connection between the semi group and the group defined by thesame presentation. The general results from Chapters 6, 7, 9 and 10 are appliedin Chapters 8, 11, 12 and 13 to subsemigroups of free semigroups, Fibonaccisemigroups, semigroups defined by Coxeter type presentations and one relatorproducts of cyclic groups. Finally, in Chapter 14 we describe the Todd-Coxeterenumeration procedure and introduce three modifications of this procedure.

[发布机构] University:University of St Andrews;Department:Mathematics & Statistics (School of)

[效力级别] Representations of groups

[关键词] Group theory;Representations of groups;Semigroups