Group and Ring Theoretic Properties of Polycyclic Groups
Wehrfritz, B.A.F.
creator
author.
SpringerLink (Online service)
text
xxk
2009
monographic
eng
access
VIII, 128 p. online resource.
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.
Some Basic Group Theory -- The Basic Theory of Polycyclic Groups -- Some Ring Theory -- Soluble Linear Groups -- Further Group-Theoretic Properties of Polycyclic Groups -- Hypercentral Groups and Rings -- Groups Acting on Finitely Generated Commutative Rings -- Prime Ideals in Polycyclic Group Rings -- The Structure of Modules over Polycyclic Groups -- Semilinear and Skew Linear Groups.
by B.A.F. Wehrfritz.
Mathematics
Associative rings
Rings (Algebra)
Commutative algebra
Commutative rings
Group theory
Mathematics
Group Theory and Generalizations
Associative Rings and Algebras
Commutative Rings and Algebras
QA174-183
512.2
Springer eBooks
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