Group and Ring Theoretic Properties of Polycyclic Groups

• Main Author: Wehrfritz, B.A.F (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2009.
• Series: Algebra and Applications ; 10
• Subjects: Mathematics.; Associative rings.; Rings (Algebra).; Commutative algebra.; Commutative rings.; Group theory.; Group Theory and Generalizations.; Associative Rings and Algebras.; Commutative Rings and Algebras.

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...

Table of Contents:

• 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.