| EPSRC Reference: |
GR/R96637/01 |
| Title: |
PROBABILISTIC GROUP THEORY AND APPLICATIONS |
| Principal Investigator: |
Liebeck, Professor M |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 September 2002 |
Ends: |
31 August 2004 |
Value (£): |
42,471
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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1. In the past few years, probabilistic methods have been introduced and used in the study of residual properties of free groups and free products of finite groups. We propose to expand and develop this approach to study residual properties of other types of infinite groups, in particular free products with amalgamation, and one-relator groups with torsion.2. Fixed point ratios of elements of primitive permutation groups have been much studied in recent years. The focus has been on upper bounds for these ratios, of which there have been some important applications. We propose to begin a study of lower bounds for fixed point ratios, which seems to be an interesting but unexplored area.3. Pyber's base conjecture states that a primitive permutation group G of degree n should have a base of size at most c log IGI / log n, where c is an absolute constant. There has been a lot of recent progress, but one major case (the affine imprimitive case') remains completely open. We propose to work on this and attempt to complete the proof of the conjecture.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.imperial.ac.uk |