| EPSRC Reference: |
GR/N28313/01 |
| Title: |
DECIDABILITY AND COMPUTABILITY IN ONE-RELATOR PRODUCTS AND GRAPHS OF GROUPS |
| Principal Investigator: |
Duncan, Dr A |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics and Statistics |
| Organisation: |
Newcastle University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
30 May 2000 |
Ends: |
29 August 2000 |
Value (£): |
2,914
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
There are 2 parts to the programme.1) decision problems. Quadratic exponential equations have been shown to be solvable in free groups and in free products of free groups with cyclic amalgamation by Comerford and Edmunds, in certain one-relator products of groups, by the applicant and in Hyperbolic groups by Friel and the applicant. The programme is to extend these solvability results to further classes of groups and to investigate the role of quadratic exponential equations in the framework of algebaric geometry of groups, as developed by Baumslag, Myasnikov, Remeslennikov and others. 2) Coherence. A group is said to be cherent if its finitely generated subgroups have finite presentations. Around 30 years ago G Baumslag asked whether one-relator groups are coherent. Until recently little progress had been made on this question. However McCammond and Wise have now shown that a one-relator group is coherent if the relator is a sufficiently high power. The programme is to generalise the result of McCammond and Wise to one-relator products to coherence of HNN-extensions and amalgamated free products of groups with coherent factors.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.ncl.ac.uk |