Name
Abstract | ||
|---|---|---|
We consider algorithms in finite groups, given by a list of generators. We give polynomial time Las Vegas algorithms (randomized, with guaranteed correct output) for basic problems for finite matrix groups over the rationals (and over algebraic number fields): testing membership, determining the order, finding a presentation (generators and relations), and finding basic building blocks: center, composition factors, and Sylow subgroups. These results extend previous work on permutation groups into the potentially more significant domain of matrix groups. Such an extension has until recently been considered intractable. In case of matrix groups G of characteristic p, there are two basic types of obstacles to polynomial-time computation: number theoretic (factoring, discrete log) and large Lie-type simple groups of the same characteristic p involved in the group. The number theoretic obstacles are inherent and appear already in handling abelian groups. They can be handled by moderately efficient (subexponential) algorithms. We are able to locate all the nonabelian obstacles in a normal subgroup N and solve all problems listed above for G/N. |
Year | DOI | Venue |
|---|---|---|
1993 | 10.1109/SFCS.1993.366844 | FOCS |
Keywords | Field | DocType |
Lie algebras,polynomial matrices,randomised algorithms,Las Vegas algorithms,Lie-type simple groups,Sylow subgroups,abelian groups,algebraic number fields,center,composition factors,finite groups,matrix groups,number theoretic obstacles,permutation groups,randomized algorithm,testing membership | Discrete mathematics,Abelian group,Combinatorics,Sylow theorems,Classification of finite simple groups,Group theory,Permutation group,Algorithm,Normal subgroup,Mathematics,Simple group,Matrix group | Conference |
ISBN | Citations | PageRank |
0-8186-4370-6 | 20 | 1.90 |
References | Authors | |
15 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| R. Beals | 1 | 20 | 1.90 |
| Laszlo Babai | 2 | 3537 | 573.58 |