Fast constructive recognition of black box unitary groups∗

Fast constructive recognition of black box symplectic groups

We present an algorithm which, for any given black box group G isomorphic to Sp(d, q), constructs explicit inverse isomorphisms between G and the standard copy of Sp(d, q). We also report on the performance of an implementation of this algorithm in the group theory system GAP.

Fast constructive recognition of black box orthogonal groups

We present an algorithm that constructively recognises when a given black box group is a nontrivial homomorphic image of the orthogonal group Ωε(d, q) for known ε, d and q. The algorithm runs in polynomial time assuming oracles for handling SL(2, q) subgroups and discrete logarithms in F∗q . © 2006 Elsevier Inc. All rights reserved.

On Constructive Recognition

Assuming the availability of an oracle for handling black box groups isomorphic to SL(2, q), we present an algorithm that constructively recognises a group G known to be isomorphic to PSL(d, q) for known d ≥ 3 and q. We also outline an analogous result for symplectic groups.

On constructive recognition of a black box PSL

Assuming the availability of an oracle for handling black box groups isomorphic to SL 2 , we present an algorithm that constructively recognises a group known to be isomorphic to PSL for known 3 and . We also outline an analogous result for symplectic groups. 1991 Mathematics Subject Classification: primary 20C40, 20G40, 20P06; secondary 51F25.

On Constructive Recognition of a Black Box PSL(d,q)