Minimality of Group and Monoid Presentations

Book : Minimality of Group and Monoid Presentations

Author : * --

Language : English

Episode : Other

Publishing Location : Glasgow

Published Date : Aralık 2007

Publisher : --

Language : Turkish

Document Type : Thesis

Book No : 5278

INDEX

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Contents
Statement
Acknowledgements
Abstract

Notation
1 Preliminaries
1.1 Words . .
1.2 Group presentations.....................
.1.2.1 Tietze transformations................
1.2.2 Pictures over group presentations..........
1.2.3 Aspherical and Cockcroft presentations.......
1.2.4 Efficiency of group presentations.......... .
1.3 Monoid presentations.....................
1.3.1 Fox derivations....................
1.3.2 Pictures over monoid presentations.........
1.3.3 Aspherical and Cockcroft monoid presentations . .
1.3.4 Efficiency of monoid presentations..........
2 The Cockcroft property of central extensions of groups
2.1 Introduction..........................
2.2 Central extensions ......................
2.3 The p-Cockcroft property for the central extensions...........
2.3.1 The general theorem........................
2.3.2 The generating pictures of tt^P).................
2.3.3 The proof of Theorem 2.3.1.............
2.4 Some examples........................
3 The efficiency of standard wreath products of groups
3.1 Some background..............................
3.2 The main theorem.............................
3.2.1 Calculation of d{H2{BA)) and 8{B A)............. ■
3.2.2 To obtain an efficient presentation for G = B A........ .
3.3 Examples and applications.........................
4 The p-Cockcroft property of the semi-direct products of monoids
4.1 Introduction.................................
4.2 Monoid presentations............................
4.2.1 Homomorphisms of monoids defined by presentations......
4.2.2 Presentations of given monoids ..................
4.2.3 Endomorphisms of monoids....................
4.3 Semi-clirect products of monoids......................
4.3.1 The definition............................
4.3.2 A generating set for D.......................
4.3.3 A presentation for D........................
4.3.4 Trivializer of the Squier complex V(Vd) .............
4.3.5 Defining a homomorphism 6 : A —V End(K)...........
4.4 The p-Cockcroft property for semi-direct products............
4.4.1 The general theorem........................
4.4.2 Direct products...........................
4.4.3 Semi-clirect products of finite cyclic monoids...........
5 Minimal presentations of semi-direct products of some monoids
5.1 Introduction............................, . . .
5.2 Semi-direct products of one-relator monoids by infinite cyclic monoids 5.2.1 The p-Cockcroft property....................
5.3 Some minimal but inefficient presentations...............