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Groups and Computation II
Edited by: Larry Finkelstein, Northeastern University, Boston, MA, and William M. Kantor, University of Oregon, Eugene, OR
A co-publication of the AMS and DIMACS.

DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
1997; 382 pp; hardcover
Volume: 28
ISBN-10: 0-8218-0516-9
ISBN-13: 978-0-8218-0516-9
List Price: US$96
Member Price: US$76.80
Order Code: DIMACS/28
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The workshop "Groups and Computations" took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop (see Groups and Computation, Finkelstein and Kantor, ©1993, American Mathematical Society) held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions.

The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).


Graduate students and research mathematicians interested in computational methods.

Table of Contents

  • L. Babai -- Randomization in group algorithms: Conceptual questions
  • G. Baumslag and C. M. III -- Experimenting and computing with infinite groups
  • R. Beals -- Towards polynomial time algorithms for matrix groups
  • F. Celler and C. R. Leedham-Green -- Calculating the order of an invertible matrix
  • F. Celler and C. R. Leedham-Green -- A non-constructive recognition algorithm for the special linear and other classical groups
  • G. Cooperman -- GAP/MPI: Facilitating parallelism
  • G. Cooperman, L. Finkelstein, and S. Linton -- Constructive recognition of a black box group isomorphic to \(GL(n,2)\)
  • B. Eick -- Special presentations for finite soluble groups and computing (pre-)Frattini subgroups
  • T. Grüner, R. Laue, and M. Meringer -- Algorithms for group actions applied to graph generation
  • J. S. Leon -- Partitions, refinements, and permutation group computation
  • E. H. Lo -- A polycyclic quotient algorithm
  • E. M. Luks and Seress -- Computing the Fitting subgroup and solvable radical for small-base permutation groups in nearly linear time
  • D. K. Maslen and D. M. Rockmore -- Generalized FFT's--A survey of some recent results
  • T. Miyazaki -- The complexity of McKay's canonical labeling algorithm
  • P. Morje -- On nearly linear time algorithms for Sylow subgroups of small base permutation groups
  • A. C. Niemeyer and C. E. Praeger -- Implementing a recognition algorithm for classical groups
  • G. Ostheimer -- Algorithms for polycyclic-by-finite matrix groups
  • L. Pyber -- Asymptotic results for simple groups and some applications
  • D. M. Rockmore -- Some applications of generalized FFT's
  • M. Tselman -- Computing permutation representations for matrix groups in parallel environments
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