| EPSRC Reference: |
GR/R71306/01 |
| Title: |
PROBABILISTIC METHODS IN GROUP THEORY |
| Principal Investigator: |
Liebeck, Professor M |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
09 October 2001 |
Ends: |
08 October 2002 |
Value (£): |
3,140
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The Magnus problem , first posed in the 1960s, states that a free group of rank at least 2 is residually in any infinite collection of finite simple groups. Many authors worked on this until it was finally proved by Weigel in 1993. A few years after this, Dixon, Pyber, Shalev and Seress found a short new proof of the Magnus problem using probabilistic methods. The proposed Visiting Fellow Shalev, and I, have recently developed these probabilistic methods to study analogous residual questions for free products A`B of non-trivial finite groups A, B. For example, we have shown that the modular group C2 C3 = PSL(2,Z) is residually in any infinite collection of finite simple groups, excluding Suzuki groups Sz(q) and 4-dimensional symplectic groups PSp(4,q) with q a power of 2 or 3. We have begun a study of the free product A'B for general A, B, and our main aim is to complete the proof that provided A, B are not both of order 2, such a free product is residually in any infinite collection of finite simple groups of unbounded rank; we currently have a proof of this, assuming that A,B are not both 2groups, a case which seems to require a new method.
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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 |
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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 |