Topics in Infinite Group Theory : : Nielsen Methods, Covering Spaces, and Hyperbolic Groups / / Benjamin Fine, Leonard Wienke, Anja Moldenhauer, Gerhard Rosenberger.

• Superior document: Title is part of eBook package: De Gruyter DG Ebook Package English 2021
• VerfasserIn: Fine, Benjamin,; Moldenhauer, Anja,; Rosenberger, Gerhard,; Wienke, Leonard,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2021]; ©2021
• Year of Publication: 2021
• Language: English
• Series: De Gruyter STEM
• Physical Description: 1 online resource (X, 382 p.)
• Other title: Frontmatter --; Preface --; Contents --; 1 Nielsen Methods --; 2 Covering Spaces --; 3 Hyperbolic Groups --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110673371; 9783110750720; 9783110750706; 9783110754001; 9783110753776; 9783110754131; 9783110753905
• DOI: 10.1515/9783110673371
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Benjamin Fine, Leonard Wienke, Anja Moldenhauer, Gerhard Rosenberger.

This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems.