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Friends and relatives of BS(1,2)
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Charles F. Miller III
Published/Copyright:
October 9, 2014
Abstract
Algorithms, constructions and examples are of central interest in combinatorial and geometric group theory. Teaching experience and, more recently, preparing a historical essay have led me to think the familiar group BS(1,2) is an example of fundamental importance. The purpose of this note is to make a case for this point of view. We recall several interesting constructions and important examples of groups related to BS(1,2), and indicate why certain of these groups played a key role in showing the word problem for finitely presented groups is unsolvable.
Received: 2013-12-19
Published Online: 2014-10-9
Published in Print: 2014-11-1
© 2014 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Editorial
- Friends and relatives of BS(1,2)
- Reflections on some aspects of infinite groups
- Generalized small cancellation presentations for automatic groups
- Diophantine cryptography in free metabelian groups: Theoretical base
- Palindromic width of wreath products, metabelian groups, and max-n solvable groups
- Group-theoretic orbit decidability
- Decoy-based information security
Keywords for this article
Word problem for groups;
Baumslag–Solitar groups;
Higman's non-hopfian group
Articles in the same Issue
- Frontmatter
- Editorial
- Friends and relatives of BS(1,2)
- Reflections on some aspects of infinite groups
- Generalized small cancellation presentations for automatic groups
- Diophantine cryptography in free metabelian groups: Theoretical base
- Palindromic width of wreath products, metabelian groups, and max-n solvable groups
- Group-theoretic orbit decidability
- Decoy-based information security
