Presentations of finite simple groups: a quantitative approach
Presentations of finite simple groups: a quantitative approach
There is a constant such that all nonabelian finite simple groups of rank over , with the possible exception of the Ree groups , have presentations with at most generators and relations and total length at most . As a corollary, we deduce a conjecture of Holt: there is a constant such that for every finite simple group , every prime and every irreducible -module .
711-774
Guralnick, R. M.
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Kantor, W. M.
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Kassabov, M.
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Lubotzky, A.
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February 2008
Guralnick, R. M.
6fef160f-e832-46da-bdf6-1363f6d5c028
Kantor, W. M.
ac564a92-9b93-4abc-9266-3f3ec9878fc9
Kassabov, M.
c0b792ea-3ac5-41b8-9883-9398114eb549
Lubotzky, A.
b89c8821-4d60-428e-a84e-ec923d2396f5
Guralnick, R. M., Kantor, W. M., Kassabov, M. and Lubotzky, A.
(2008)
Presentations of finite simple groups: a quantitative approach.
Journal of the American Mathematical Society, 21, Winter Issue, .
(doi:10.1090/S0894-0347-08-00590-0).
Abstract
There is a constant such that all nonabelian finite simple groups of rank over , with the possible exception of the Ree groups , have presentations with at most generators and relations and total length at most . As a corollary, we deduce a conjecture of Holt: there is a constant such that for every finite simple group , every prime and every irreducible -module .
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Published date: February 2008
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Funded by:
National Science Foundation: Arithmetic Groups (354731)
National Science Foundation: Linear and Permutation Representations of Groups and Coverings of Curves (140578)
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Local EPrints ID: 155177
URI: http://eprints.soton.ac.uk/id/eprint/155177
ISSN: 0894-0347
PURE UUID: 1f098ec8-05fa-4270-9376-ffbc17f0c150
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Date deposited: 27 May 2010 10:56
Last modified: 14 Mar 2024 01:37
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Author:
R. M. Guralnick
Author:
W. M. Kantor
Author:
M. Kassabov
Author:
A. Lubotzky
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