Listing 1 - 4 of 4 |
Sort by
|
Choose an application
Choose an application
Choose an application
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.
Choose an application
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.
Graph theory. --- Polycyclic groups. --- Rings (Algebra). --- Solvable groups. --- Polycyclic groups --- Solvable groups --- Graph theory --- Rings (Algebra) --- Mathematics --- Algebra --- Physical Sciences & Mathematics --- Algebraic rings --- Ring theory --- Graphs, Theory of --- Theory of graphs --- Extremal problems --- Mathematics. --- Associative rings. --- Commutative algebra. --- Commutative rings. --- Group theory. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Commutative Rings and Algebras. --- Algebraic fields --- Combinatorial analysis --- Topology --- Infinite groups --- Nilpotent groups --- Algebra. --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics)
Listing 1 - 4 of 4 |
Sort by
|