The Theory of Nilpotent Groups

This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.

List of contents

Commutator Calculus.- Introduction to Nilpotent Groups.- The Collection Process and Basic Commutators.- Normal Forms and Embeddings.- Isolators, Extraction of Roots, and P -Localization.- "The Group Ring of a Class of Infinite Nilpotent Groups" by S. A. Jennings.- Additional Topics.

Summary

Collects both classical and recent results into a single, comprehensive source
Provides all necessary proofs in full detail
Can be used as a standard reference on the topic by both graduate students and researchers

Product details

• Authors: Anthony Clement, Anthony E Clement, Anthony E. Clement, Stephe Majewicz, Stephen Majewicz, Marcos Zyman
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 31.12.2017
• EAN: 9783319662114
• ISBN: 978-3-31-966211-4
• No. of pages: 307
• Dimensions: 157 mm x 243 mm x 24 mm
• Weight: 662 g
• Illustrations: XVII, 307 p.
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, B, Group Theory, Mathematics and Statistics, Topological Groups, Lie Groups, Rings (Algebra), Topological groups, Lie groups, Topological Groups and Lie Groups, Groups & group theory, Group Theory and Generalizations, Associative rings, Associative Rings and Algebras