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Abstract: We announce methods for efficient management of solvable matrix groups over finite fields. We show that solvability and nilpotencecan betestedin polynomial-time. Such efficiency seems unlikely for membership-testing, which subsumes the discrete-log problem. However, assuming that the primes in jGj (other than the field characteristic) arepolynomiallybounded, membership-testing and many other computational problems areinpolynomial time. These problems include finding stabilizers of vectors and... (Update)
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.... in polynomial time (Kantor and Luks, 1990) More generally, normalizers are computable in polynomial time even for solvable groups (Luks, 1992). With this background in mind, we describe a normalizer algorithm for nilpotent subgroups of Sn that has worst case timing of O(n 4...
...should mention that various other properties (whether G is nilpotent, solvable, etc. have been studied in various settings (see [BCPLS,CP1,CP2,L1]) Our randomized algorithm, when used a routine, easily improves complexity of some of these advanced algorithms. Before we nish,...
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Computing with Matrix Groups - Kantor, Seress (2001) (Correct)
A Note on tThe Subgroup Membership Problem for PSL(2,p) - Charles (2001) (Correct)
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BibTeX entry: (Update)
E. M. Luks, "Computing in Solvable Matrix Groups", Proc. 33 rd IEEE FOCS (1992), pp. 111--120. http://citeseer.ist.psu.edu/luks92computing.html More
@inproceedings{ luks92computing,
author = "Eugene M. Luks",
title = "Computing in Solvable Matrix Groups",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "111-120",
year = "1992",
url = "citeseer.ist.psu.edu/luks92computing.html" }
Citations (may not include all citations):173 Trading group theory for randomness (context) - Babai - 1985
82 The Theory of Groups (context) - Hall - 1959
49 Isomorphism of graphs of bounded valence can betestedinpolyn.. (context) - Luks - 1982
39 Polynomial time algorithms for permutation groups (context) - Furst, Hopcroft et al. - 1980
24 Algorithms and Programming (context) - Schonert, Groups - 1992
23 the complexity of matrix group problems (context) - Babai, Szemer'edi - 1984
18 Permutation groups in NC (context) - Babai, Luks et al. - 1987
13 Computing in quotient groups - Kantor, Luks - 1990
13 Sylow's theorem in polynomial time (context) - Kantor - 1985
8 An introduction to the group theory language Cayley (context) - Cannon - 1984
6 Parallel algorithms for permutation groups and graph isomorp.. (context) - Luks - 1986
5 Number-theoretic algorithms (context) - Bach
5 Matrix Groups (context) - Suprunenko - 1976
4 Rockmore Deciding finiteness of matrix groups in determinist.. (context) - Babai, Beals - 1992
4 Some group-theoretic algorithms (context) - Sims - 1978
4 Isomorphism of graphs which arepairwise k-separable (context) - Miller - 1983
4 The occurrenceproblem for direct products of group (context) - Mihailova - 1966
3 Computational Problems in Abstract Algebra (context) - Leech - 1970
2 The Schreier algorithm for matrix groups (context) - Butler - 1976
2 Computing the structure of finite algebras (context) - R'onyai - 1990
2 Parallel algorithms for solvable permutation groups (context) - Luks, McKenzie - 1988
2 Sylow's theorem and parallel computation (context) - Mark - 1992
2 Computational Group Theory (context) - Atkinson - 1984
1 Apolynomial bound on the orders of primitive solvable groups (context) - P'alfy - 1982
1 Finding Sylow normalizers in polynomial time J (context) - Kantor - 1990
1 Seress Fast Monte Carlo algorithms for permutation groups (context) - Babai, Cooperman et al. - 1991
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.cs.uoregon.edu/~luks/):
Computing the Composition Factors of a Permutation Group in.. - Luks (1987) (Correct)
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