Abstract:
Abstract. We report some results on deterministic algorithms for efficient management of matrix groups over finite fields. Our results generalize Luks's work on solvable matrix groups to wider classes of matrix groups. In this article, we present algorithms for membership-testing and its closely related problems. The algorithms run deterministically in time polynomial in these three parameters: the input length of given generators for a matrix group G, the largest prime dividing
Citations
|
90
|
Isomorphism of graphs of bounded valence and be tested in polynomial time
– Luks
- 1982
|
|
53
|
A Course in the Theory of Groups
– Robinson
- 1995
|
|
32
|
Polynomial-time algorithms for permutation groups
– Furst, Hopcroft, et al.
- 1980
|
|
30
|
Computational methods in the study of permutation groups
– Sims
- 1967
|
|
27
|
A polynomial-time theory of black box groups. I, Groups St An-drews 1997 in
– BABAI, BEALS
- 1997
|
|
21
|
Las Vegas algorithms for matrix groups
– Beals, Babai
- 1993
|
|
15
|
Computing in quotient groups
– Kantor, Luks
- 1990
|
|
14
|
Permutation groups, Graduate Texts
– Dixon, Mortimer
- 1996
|
|
10
|
On the orders of primitive groups with restricted nonabelian composition factors
– BABAI, CAMERON, et al.
- 1982
|
|
9
|
Testing equalities of multiplicative representations in polynomial time
– GE
- 1993
|
|
7
|
Zalcstein: The complexity of the membership problem for 2-generated commutative semigroups of rational matrices
– Cai, Lipton, et al.
- 1994
|
|
6
|
Multiplicative equations over commuting matrices
– BABAI, BEALS, et al.
- 1996
|
|
6
|
Towards polynomial time algorithms for matrix groups, Groups and Computation
– BEALS
- 1997
|
|
3
|
Chains of subgroups in groups of Lie type
– Solomon, Turull
- 1990
|
|
2
|
Polynomial-time computation in matrix groups
– MIYAZAKI
- 1999
|
|
2
|
Matrix groups, "Nauka
– SUPRUNENKO
- 1972
|
