Polycyclic Groups

This book will be of interest to mathematicians doing research in algebra, and to postgraduate students studying that subject.

Daniel Segal (Author)

9780521023948, Cambridge University Press

Paperback / softback, published 17 November 2005

304 pages
22.9 x 15.5 x 1.9 cm, 0.461 kg

The theory of polycyclic groups is a branch of infinite group theory which has a rather different flavour from the rest of that subject. This book is a comprehensive account of the present state of this theory. As well as providing a connected and self-contained account of the group-theoretical background, it explains in detail how deep methods of number theory and algebraic group theory have been used to achieve some very recent and rather spectacular advances in the subject. Up to now, most of this material has only been available in scattered research journals, and some of it is new. This book is the only unified account of these developments, and will be of interest to mathematicians doing research in algebra, and to postgraduate students studying that subject.

Preface
Notation
1. The elements, 2. Mal'cev's theorems
3. Extensions
4. Arithmetical methods
5. Faithful representations
6. On unipotent groups
7. Semi-simple splitting
8. Soluble Z-linear groups
9. A finiteness theorem
10. Polycyclic groups with isomorphic finite quotients
11. Examples
Appendix
References
Index.

Subject Areas: Algebra [PBF]