**DIMACS - Series in Discrete Mathematics and Theoretical Computer Science**

Volume: 11;
1993;
313 pp;
Hardcover

MSC: Primary 20;

Print ISBN: 978-0-8218-6599-6

Product Code: DIMACS/11

List Price: $89.00

Individual Member Price: $71.20

**Electronic ISBN: 978-1-4704-3969-9
Product Code: DIMACS/11.E**

List Price: $89.00

Individual Member Price: $71.20

# Groups and Computation

Share this page *Edited by *
*Larry Finkelstein; William M. Kantor*

A co-publication of the AMS and DIMACS

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

## Groups and Computation

- Cover Cover11
- Title page v6
- Dedication vii8
- Contents ix10
- Foreword xi12
- Preface xiii14
- Workshop Program xv16
- Participants xvii18
- Computing composition series in primitive groups 122
- Computing blocks of imprimitivity for small-base groups in nearly linear time 1738
- Fast Fourier transforms for symmetric groups 2748
- From hyperbolic reflections to finite groups 4162
- Combinatorial tools for computational group theory 5374
- Efficient computation of isotypic projections for the symmetric group 87108
- Constructing representations of finite groups 105126
- A graphics system for displaying finite quotients of finitely presented groups 113134
- Random remarks on permutation group algorithms 127148
- Application of group theory to combinatorial searches 133154
- Permutation groups and polynomial-time computation 139160
- Parallel computation of Sylow subgroups in solvable groups 177198
- Computation with matrix groups over finite fields 189210
- Asymptotic results for permutation groups 197218
- Computations in associative algebras 221242
- Cayley graphs and direct-product graphs 245266
- Group membership for groups with primitive orbits 253274
- PERM: a program computing strong generating sets 269290
- Complexity issues in infinite group theory 277298
- GRAPE: a system for computing with graphs and groups 287308
- Implications of parallel architectures for permutation group computations 293314
- Back Cover Back Cover1335