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Abstract: We present polynomial-time algorithms for computation in quotient groups G=K of a permutation group G. In effect, these solve, for quotient groups, the problems that are known to be in polynomial-time for permutation groups. Since it is not computationally feasible to represent G=K itself as a permutation group, the methodology for the quotient-group versions of such problems frequently differ markedly from the procedures that have been observed for the K = 1 subcases. Whereas the algorithms... (Update)
Context of citations to this paper: More
...a finite group for which we want to determine the normal subgroups. We start with a chief series for G. Such a series can be computed [13, 11] by forming the # Supported by EPSRC Grant GL L21013 intersection of conjugates in a composition series of G (this yields a series of...
.... [5] This has motivated extensive investigation into polynomial time computability for permutation group problems in general (see [13], 19] for surveys) but especially for Problems A D. Now, aside from the overall reducibility between the above problems, solutions...
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BibTeX entry: (Update)
Kantor, W.M., Luks, E.M. (1990). Computing in quotient groups. Proc. 22 nd ACM Symposium on Theory of Computing, 524--533. http://citeseer.ist.psu.edu/kantor90computing.html More
@inproceedings{ kantor90computing,
author = "William M. Kantor and Eugene M. Luks",
title = "Computing in Quotient Groups",
booktitle = "{ACM} Symposium on Theory of Computing",
pages = "524-534",
year = "1990",
url = "citeseer.ist.psu.edu/kantor90computing.html" }
Citations (may not include all citations):110 Proofs that yield nothing but their validity and a methodolo.. (context) - Goldreich, Micali et al. - 1986
82 The Theory of Groups (context) - Hall - 1959
80 Finite Permutation Groups (context) - Wielandt - 1964
79 Arthur-Merlin games: A randomized proof system and a hierarc.. (context) - Babai, Moran - 1988
49 Isomorphism of graphs of bounded valence can be tested in po.. (context) - Luks - 1982 DBLP
39 Polynomial time algorithms for permutation groups (context) - Furst, Hopcroft et al. - 1980
29 Group Theoretic Algorithms and Graph Isomorphism (context) - Hoffmann - 1982
26 Canonical labeling of graphs (context) - Babai, Luks - 1983 ACM DBLP
23 the complexity of matrix group problems (context) - Babai, Szemer'edi - 1984
22 Fast management of permutation groups (context) - Babai, Luks et al. - 1988 DBLP
18 Permutation groups in NC (context) - Babai, Luks et al. - 1987 ACM DBLP
16 nauty User's Guide (context) - McKay - 1987
16 Moderately exponential bound for graph isomorphism (context) - Babai - 1981 ACM DBLP
15 Monte Carlo algorithms for graph isomorphism testing (context) - Babai - 1979
14 Computational complexity and the classification of finite si.. (context) - Babai, Kantor et al. - 1983 DBLP
13 Sylow's theorem in polynomial time (context) - Kantor - 1985 DBLP
13 Harper and Row (context) - Gorenstein, Groups - 1968
11 Canonical labelling of graphs in linear average time (context) - Babai, Kucera - 1979 DBLP
9 an algorithm for finding a base and strong generating set fo.. (context) - Leon - 1980
9 Computing the composition factors of a permutation group in .. - Luks - 1987 ACM DBLP
8 the order of primitive groups with restricted nonabelian com.. (context) - Babai, Cameron et al. - 1982
8 An introduction to the group theory language Cayley (context) - Cannon - 1984
6 Computing the structure of finite algebras (context) - R'onyai - 1989 ACM DBLP
5 the length of subgroup chains in the symmetric group (context) - Babai - 1986
5 Polynomial-time algorithms for finding elements of prime ord.. (context) - Kantor - 1985 DBLP
5 a generalization of bounded valence and bounded genus (context) - Miller, k-contractible - 1983
4 Some group-theoretic algorithms (context) - Sims - 1978
4 Isomorphism of graphs which are pairwise k-separable (context) - Miller - 1983 DBLP
4 Normal forms for trivalent graphs and graphs of bounded vale.. (context) - Furer, Schnyder et al. - 1983 ACM DBLP
4 Canonical labeling of regular graphs in linear average time (context) - Kucera - 1987 DBLP
3 Finding Sylow normalizers in polynomial time (context) - Kantor ACM DBLP
3 Polynomial-time versions of Sylow's theorem (context) - Kantor, Taylor - 1988 ACM DBLP
3 Reduction of group constructions to point stabilizers (context) - Cooperman, Finkelstein et al. - 1989 ACM DBLP
1 A Las Vegas-NC algorithm for isomorphism of graphs with boun.. (context) - Babai - 1986 DBLP
1 Algorithms for quotients of permutation groups (context) - Kantor, Luks
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