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Combinatorial Group Theory
Open Problems on Infinite Groups
Series: De Gruyter Textbook
Brief Description
This is an annotated collection of over 200 open problems in combinatorial group theory. One can say that most of the problems are closer in spirit to the "purely combinatorial" group theory. However, the authors included several problems with geometric flavour where they felt this was...
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Combinatorial Group Theory
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Description
This is an annotated collection of over 200 open problems in combinatorial group theory. One can say that most of the problems are closer in spirit to the "purely combinatorial" group theory. However, the authors included several problems with geometric flavour where they felt this was natural.
Approximately 20 years ago, a new direction in group theory began to emerge at the interface with theoretical computer science. In recognition of this, the given collection includes problems that are not only significant in combinatorial group theory but also have direct relevance to this emerging area, such as the Post correspondence problem for groups, which is gaining momentum in contemporary research.
The “flagship” section includes problems about free groups; these have been at the centre of combinatorial group theory for over a century, and they are getting ever more popular due to newly discovered connections with the theoretical computer science mentioned above.
Other classes of groups that the authors cover include hyperbolic groups, solvable groups, groups of matrices, and others. The target audience of the book is very broad: from PhD students to senior researchers.
Combinatorial Group Theory offers valuable insights and challenges for those interested in the field. Whether you are a newcomer or a seasoned researcher, the book provides a comprehensive outlook on both established and emerging areas of study.
Series: De Gruyter Textbook
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Book Details
INFORMATION
ISBN: 9783119146791
Publisher: De Gruyter
Format: Paperback / softback
Date Published: 16 March 2026
Country: Germany
Imprint: De Gruyter
Audience: Tertiary education
DIMENSIONS
Width: 170.0mm
Height: 240.0mm
Weight: 178g
Pages: 88
About the Author
All authors are top-notch group theorists.
Ilya Kapovich is Professor of Mathematics at the City University of New York (Hunter College). He is the author of over 80 papers and one monograph.
Alexei Myasnikov is Distinguished Professor of Mathematics at Stevens Institute of Technology. He is the author of over 200 papers and 4 monographs.
Vladimir Shpilrain is Professor of Mathematics at the City University of New York (City College). He is the author of over 120 papers and 4 monographs.
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