Group-theoretic orbit decidability
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Enric Ventura
Abstract
A recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely related to the study of the conjugacy problem for extensions of groups. In the present survey we explain several of the classical results closely related to this concept, and we explain the main ideas behind the recent connection with the conjugacy problem made by Bogopolski–Martino–Ventura in [Trans. Amer. Math. Soc. 362 (2010), 2003–2036]. All the consequences up to date, published in several other papers by other authors, are also commented and reviewed.
Funding source: Spanish Government
Award Identifier / Grant number: MTM2011-25955
© 2014 by De Gruyter
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
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
