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Groups and Computation
Edited by: Larry Finkelstein and William M. Kantor
A co-publication of the AMS and DIMACS.
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DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
1993; 313 pp; hardcover
Volume: 11
ISBN-10: 0-8218-6599-4
ISBN-13: 978-0-8218-6599-6
List Price: US$84 Member Price: US$67.20
Order Code: DIMACS/11

This volume contains papers presented at the Workshop on Groups and Computation, held in October 1991. The workshop explored interactions among four areas: symbolic algebra and computer algebra, theoretical computer science, group theory, and applications of group computation. The relationships between implementation and complexity form a recurrent theme, though the papers also discuss such topics as parallel algorithms for groups, computation in associative algebras, asymptotic behavior of permutation groups, the study of finite groups using infinite reflection groups, combinatorial searching, computing with representations, and Cayley graphs as models for interconnection networks.

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).

Readership

Research mathematicians and computer scientists.

Table of Contents

• L. Babai, E. M. Luks, and Seress -- Computing composition series in primitive groups
• R. Beals -- Computing blocks of imprimitivity for small-base groups in nearly linear time
• M. Clausen and U. Baum -- Fast Fourier transforms for symmetric groups
• J. H. Conway -- From hyperbolic reflections to finite groups
• G. Cooperman and L. Finkelstein -- Combinatorial tools for computational group theory
• P. Diaconis and D. Rockmore -- Efficient computation of isotypic projections for the symmetric group
• J. D. Dixon -- Constructing representations of finite groups
• D. F. Holt and S. Rees -- A graphics system for displaying finite quotients of finitely presented groups
• W. M. Kantor -- Random remarks on permutation group algorithms
• C. W. H. Lam -- Application of group theory to combinatorial searches
• E. M. Luks -- Permutation groups and polynomial-time computation
• P. D. Mark -- Parallel computation of Sylow subgroups in solvable groups
• C. E. Praeger -- Computation with matrix groups over finite fields
• L. Pyber -- Asymptotic results for permutation groups
• L. Rónyai -- Computations in associative algebras
• A. L. Rosenberg -- Cayley graphs and direct-product graphs
• N. Sarawagi, G. Cooperman, and L. Finkelstein -- Group membership for groups with primitive orbits
• Seress and I. Weisz -- PERM: A program computing strong generating sets
• C. C. Sims -- Complexity issues in infinite group theory
• L. H. Soicher -- GRAPE: A system for computing with graphs and groups
• B. W. York -- Implications of parallel architectures for permutation group computations
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