Conlcnls
Preface v
Lecture 1: Introductio n 1
1.1. Fre e presentations ; generator s an d relation s 1
1.2. Finit e presentabilit y 1
1.3. Thre e question s 1
1.4. Connexio n wit h extensio n theor y 2
1.5. Centra l extensions : Schur' s theor y 2
1.6. Relatio n module s 3
1.7. Surve y o f som e result s t o com e 4
1.8. Relatio n module s modul o p 5
Lecture 2 : Th e Gaschut z theor y 6
2.1. Th e modul e sequenc e associate d wit h a grou p extensio n 6
2.2. Compariso n o f relatio n module s modul o n 7
2.3- Th e structur e o f relatio n module s modul o p 8
2.4. Countin g projectiv e summand s i n relatio n module s modul o p 10
Lecture 3 : Modul e theoreti c preliminarie s 12
3.1. Ring s o f fraction s 12
3.2. Localizatio n 13
3.3- Modul e extension s 14
3.4. Loca l coefficien t ring s 16
Lecture 4 : Projectiv e module s 19
4.1. Genu s 19
4.2. Structur e o f locall y fre e modules ; statemen t o f Swan' s structur e
theorem fo r projectiv e module s 2 0
4.3. \ 21
AA. Proo f o f Swan' s theore m 2 2
4.5. ' - 2 3
Lecture 5 : Relatio n core s 2 6
5.1. Core s an d th e projectiv e ran k o f a lattice 2 6
5.2. Relatio n core s an d th e presentatio n ran k 2 7
5.3- Statemen t o f Roiter' s replacemen t theorem ; an d som e consequence s 2 8
5.4. Proo f o f Roiter' s theore m 3 0
5.5. Compariso n o f relatio n module s 3 1
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