Computing in solvable matrix groups

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn 1992-October, Issue , 1992, Pages 111-120

  Luks, Eugene M ^a  

^a UNIVERSITY OF OREGON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GROUP THEORY; POLYNOMIAL APPROXIMATION;

ALGEBRAIC NUMBER FIELDS; COMPUTATIONAL PROBLEM; EFFICIENT MANAGEMENTS; FINITE FIELDS; FINITE MATRICES; PERMUTATION GROUP; POLYNOMIAL-TIME; SYLOW SUBGROUP;

MATRIX ALGEBRA;

EID: 85065731689     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SFCS.1992.267813     Document Type: Conference Paper

References (26)

1. M.D. Atkinson, ed., Computational Group Theory, Academic Press, 1984.
2. L. Babai, Trading group theory for randomness, Proc. 17th ACM STOC, 1985, 421-429.
3. E. Bach, Number-theoretic algorithms, in Annual Review of Computer Science, v.4 1989-1990, Annual Reviews Inc., 119-172.
4. L. Babai, R. Beals, and D. Rockmore Deciding finite-ness of matrix groups in deterministic polynomial time, Tech Rep, U. Chicago, 1992.
5. L. Babai, G. Cooperman, L. Finkelstein, E. Luks and A. Seress Fast Monte Carlo algorithms for permutation groups, 23rd ACM STOC, 1991, 90-100.
6. L. Babai, E.M. Luks and A. Seress, Permutation groups in NC, Proc. 19th ACM STOC, 1987, 409-420.
7. L. Babai and E. Szemeredi, On the complexity of matrix group problems, Proc. 24th IEEE FOCS, 1984, 229-240.
8. G. Butler, The Schreier algorithm for matrix groups, in Proc. 1976 ACM Symp. on Symbolic and Algebraic Comp., 167-170.
9. J.J. Cannon, An introduction to the group theory language Cayley, in Computational Group Theory (ed. M.D. Atkinson), Academic Press 1984, 145-183.
10. M.L. Furst, J. Hopcroft and E.M. Luks, Polynomial time algorithms for permutation groups, Proc. 21th IEEE FOCS, 1980, 36-41.
11. M. Hall, Jr., The Theory of Groups, Macmillan, New York 1959.
12. W.M. Kantor, Sylow's theorem in polynomial time, J. Comp. Syst. Sci. 30 (1985) 359-394.
13. W.M. Kantor, Finding Sylow normalizers in polynomial time J. Algorithms 11 (1990), 523-563.
14. W.M. Kantor and E.M. Luks, Computing in quotient groups, 22nd ACM STOC, 1990, 524-534.
15. J. Leech, ed., Computational Problems in Abstract Algebra, Pergamon, NY, 1970.
16. E.M. Luks, Isomorphism of graphs of bounded valence can be tested in polynomial time, J. Comp. Syst. Sci. 25 (1982), 42-65.
17. E.M. Luks, Parallel algorithms for permutation groups and graph isomorphism, Proc. 27th IEEE FOCS 1986, 292-302.
18. E.M. Luks and P. McKenzie, Parallel algorithms for solvable permutation groups, J. Comp. Syst. Sci. 37 (1988), 39-62.
19. P.D. Mark, Sylow's theorem and parallel computation, Doctoral dissertation, CIS, U. Oregon, 1992.
20. K.A. Mihailova, The occurrence problem for direct products of group, Mat. Sb. (N.S.) 70(112) (1966), 241-251.
21. G.L. Miller, Isomorphism of graphs which are pairwise k-separable, Inform, and Control 56 (1983), 21-33.
22. P. Palfy, A polynomial bound on the orders of primitive solvable groups, J. Algebra, 78 (1982), 127-137.
23. L. Ronyai, Computing the structure of finite algebras, J. Symbolic Computation 9 (1990), 355-373.
24. M. Schonert et al, GAP: Groups, Algorithms and Programming, Aachen, 1992.
25. C.C. Sims, Some group-theoretic algorithms, Springer Lect. Notes in Math. 697 (1978), 108-124.
26. D.A. Suprunenko, Matrix Groups, AMS, 1976.