Recognising the Suzuki groups in their natural representations
| dc.creator | Bäärnhielm, Henrik | |
| dc.date | 2006-08-09 | |
| dc.date.accessioned | 2026-07-07T07:21:33Z | |
| dc.date.available | 2026-07-07T07:21:33Z | |
| dc.description | Under the assumption of a certain conjecture, for which there exists strong experimental evidence, we produce an efficient algorithm for constructive membership testing in the Suzuki groups Sz(q), where q = 2^{2m + 1} for some m > 0, in their natural representations of degree 4. It is a Las Vegas algorithm with running time O{log(q)} field operations, and a preprocessing step with running time O{log(q) loglog(q)} field operations. The latter step needs an oracle for the discrete logarithm problem in GF(q). We also produce a recognition algorithm for Sz(q) = <X>. This is a Las Vegas algorithm with running time O{|X|^2} field operations. Finally, we give a Las Vegas algorithm that, given <X>^h = Sz(q) for some h in GL(4, q), finds some g such that <X>^g = Sz(q). The running time is O{log(q) loglog(q) + |X|} field operations. Implementations of the algorithms are available for the computer system MAGMA. | |
| dc.identifier | https://arxiv.org/abs/math/0608210 | |
| dc.identifier | http://arxiv.org/abs/math/0608210 | |
| dc.identifier | J. Algebra 300 (1), 171-198, 2006 | |
| dc.identifier | doi:10.1016/j.jalgebra.2006.02.010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115336 | |
| dc.subject | Group Theory | |
| dc.subject | Data Structures and Algorithms | |
| dc.subject | 20H30, 68Q25, 68W20 (Primary) 20P05, 20C33, 20C40 (Secondary) | |
| dc.title | Recognising the Suzuki groups in their natural representations | |
| dc.type | text |