Group and Ring Theoretic Properties of Polycyclic Groups (eBook)

B.A.F. Wehrfritz (Autor)

eBook Download: PDF

2009 | 2009
VIII, 128 Seiten
Springer London (Verlag)
978-1-84882-941-1 (ISBN)

Infos

Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations.

The book is intended to be a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch. Thus it has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. An extensive bibliography then concludes the book.

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Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations.The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups.

Inhalt

Preface 6
Contents 8
1 Some Basic Group Theory 9
2 The Basic Theory of Polycyclic Groups 20
3 Some Ring Theory 36
4 Soluble Linear Groups 47
5 Further Group-Theoretic Properties of Polycyclic Groups 61
6 Hypercentral Groups and Rings 69
7 Groups Acting on Finitely Generated Commutative Rings 81
8 Prime Ideals in Polycyclic Group Rings 94
9 The Structure of Modules over Polycyclic Groups 104
10 Semilinear and Skew Linear Groups 113
Notation 121
Bibliography 124
Index 129

Produkt-Details

• Erscheint lt. Verlag: 28.11.2009
• Reihe/Serie: Algebra and Applications
• Reihe/Serie: Algebra and Applications
• Zusatzinfo: VIII, 128 p.
• Verlagsort: London
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• Schlagworte: Algebra • group theory • Noetherian rings • polycyclic groups • Ring Theory • Vector Space
• ISBN-10: 1-84882-941-8 / 1848829418
• ISBN-13: 978-1-84882-941-1 / 9781848829411