Let G = hXi be isomorphic to a classical matrix group H = hSi ≤ GL(d, q)in natural representation, where S is a nice generating set. For example, one can efficiently write an arbitrary element of H as a word in S. Informally, a constructive recognition algorithm constructs an effective isomorphism from G to H, and vice versa. An approach for doing this is to consider a generating set S′ ⊆ G corresponding to S, and to write the elements of S′ as words in X. If every element of G can efficiently be written as a word in S′, then the isomorphisms G ↔ H defined by S′ ↔ S are effective since images can be computed readily. For example, if g ∈ G is written as a word w(S′) in S′, then the image of g in H is easily determined as w(S). Thus, instead of working in G, this allows us to work in the nice group H.
|Title of host publication||Mathematisches Forschungsinstitut Oberwolfach|
|Subtitle of host publication||Report No. 37/2011 - Computational Group Theory|
|Place of Publication||Germany|
|Publisher||Mathematisches Forschungsinstitut Oberwolfach|
|Number of pages||2|
|Publication status||Published - 2011|