Abstract
Original language | English |
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Pages (from-to) | 371-384 |
Number of pages | 14 |
Journal | Journal of Symbolic Computation |
Volume | 46 |
DOIs | |
Publication status | Published - 2011 |
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Constructive homomorphisms for classical groups. / Murray, Scott; Roney-Dougal, Colva.
In: Journal of Symbolic Computation, Vol. 46, 2011, p. 371-384.Research output: Contribution to journal › Article
TY - JOUR
T1 - Constructive homomorphisms for classical groups
AU - Murray, Scott
AU - Roney-Dougal, Colva
PY - 2011
Y1 - 2011
N2 - Let be a quasisimple classical group in its natural representation over a finite vector space , and let . We construct the projection from to and provide fast, polynomial-time algorithms for computing the image of an element. Given a discrete logarithm oracle, we also represent as a group with at most 3 generators and 6 relations. We then compute canonical representatives for the cosets of . A key ingredient of our algorithms is a new, asymptotically fast method for constructing isometries between spaces with forms. Our results are useful for the matrix group recognition project, can be used to solve element conjugacy problems, and can improve algorithms to construct maximal subgroups.
AB - Let be a quasisimple classical group in its natural representation over a finite vector space , and let . We construct the projection from to and provide fast, polynomial-time algorithms for computing the image of an element. Given a discrete logarithm oracle, we also represent as a group with at most 3 generators and 6 relations. We then compute canonical representatives for the cosets of . A key ingredient of our algorithms is a new, asymptotically fast method for constructing isometries between spaces with forms. Our results are useful for the matrix group recognition project, can be used to solve element conjugacy problems, and can improve algorithms to construct maximal subgroups.
KW - Classical groups
U2 - 10.1016/J.JSC.2010.09.003
DO - 10.1016/J.JSC.2010.09.003
M3 - Article
VL - 46
SP - 371
EP - 384
JO - Journal of Symbolic Computation
JF - Journal of Symbolic Computation
SN - 0747-7171
ER -