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The Theory of Nilpotent Groups / by Anthony E. Clement, Stephen Majewicz, Marcos Zyman.
Springer Nature - Springer Mathematics and Statistics eBooks 2017 English International Available online
View online- Format:
- Book
- Author/Creator:
- Clement, Anthony E., Author.
- Majewicz, Stephen., Author.
- Zyman, Marcos., Author.
- Language:
- English
- Subjects (All):
- Group theory.
- Associative rings.
- Rings (Algebra).
- Topological groups.
- Lie groups.
- Group Theory and Generalizations.
- Associative Rings and Algebras.
- Topological Groups, Lie Groups.
- Local Subjects:
- Group Theory and Generalizations.
- Associative Rings and Algebras.
- Topological Groups, Lie Groups.
- Physical Description:
- 1 online resource (XVII, 307 p.)
- Edition:
- 1st ed. 2017.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
- Summary:
- 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.
- 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.
- Notes:
- Includes bibliographical references and index.
- ISBN:
- 3-319-66213-9
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