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

Volume: 28;
1997;
382 pp;
Hardcover

MSC: Primary 20;

**Print ISBN: 978-0-8218-0516-9
Product Code: DIMACS/28**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

**Electronic ISBN: 978-1-4704-3986-6
Product Code: DIMACS/28.E**

List Price: $101.00

AMS Member Price: $80.80

MAA Member Price: $90.90

# Groups and Computation II

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

A co-publication of the AMS and DIMACS

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

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).

#### Readership

Graduate students and research mathematicians interested in computational methods.

# Table of Contents

## Groups and Computation II

- Cover Cover11
- Title page v6
- Contents vii8
- Foreword ix10
- Preface xi12
- Workshop program xiii14
- Participants xv16
- Randomization in group algorithms: Conceptual questions 120
- Experimenting and computing with infinite groups 1938
- Towards polynomial time algorithms for matrix groups 3150
- Calculating the order of an invertible matrix 5574
- A non-constructive recognition algorithm for the special linear and other classical groups 6180
- GAP/MPI: Facilitating parallelism 6988
- Constructive recognition of a black box group isomorphic to 𝐺𝐿(𝑛,2) 85104
- Special presentations for finite soluble groups and computing (pre-)Frattini subgroups 101120
- Algorithms for group actions applied to graph generation 113132
- Partitions, refinements, and permutation group computation 123142
- A polycyclic quotient algorithm 159178
- Computing the fitting subgroup and solvable radical of small-base permutation groups in nearly linear time 169188
- Generalized FFTs–A survey of some recent results 183202
- The complexity of McKay’s canonical labeling algorithm 239258
- On nearly linear time algorithms for Sylow subgroups of small-base permutation groups 257276
- Implementing a recognition algorithm for classical groups 273292
- Algorithms for polycyclic-by-finite matrix groups 297316
- Asymptotic results for simple groups and some applications 309328
- Some applications of generalized FFTs 329348
- Constructing permutation representations for matrix groups in parallel environments 371390
- Back Cover Back Cover1402