Groups and Computation

by Kantor, William M.

• ISBN13: 9783110167214
• ISBN10: 3110167212
• Format: Hardcover
• Copyright: 2000-06-01
• Publisher: De Gruyter

Summary

This volume contains contributions by the participants of the conference "Groups and Computation", which took place at The Ohio State University in Columbus, Ohio, in June 1999. This conference was the successor of two workshops on "Groups and Computation" held at DIMACS in 1991 and 1995.There are papers on permutation group algorithms, finitely presented groups, polycyclic groups, and parallel computation, providing a representative sample of the breadth of Computational Group Theory. On the other hand, more than one third of the papers deal with computations in matrix groups, giving an in-depth treatment of the currently most active area of the field.The points of view of the papers range from explicit computations to group-theoretic algorithms to group-theoretic theorems needed for algorithm development.

Table of Contents

Preface
Probabilistic recognition of orthogonal and symplectic groups	p. 1
Janko's simple groups J[subscript 2] and J[subscript 3] are irreducible subgroups of SL[subscript 85](5) with equal centralizers of an involution	p. 21
Recognizing simplicity of black-box groups and the frequency of p-singular elements in affine groups	p. 39
Improved algorithms for the Tits alternative	p. 63
A constructive recognition algorithm for the matrix group [Omega](d, q)	p. 79
On constructive recognition of a black box PSL(d, q)	p. 95
Fast recognition of classical groups over large fields	p. 113
Parallel GAP: Mature interactive parallel computing	p. 123
Computing with infinite polycyclic groups	p. 139
Computing the maximal subgroups of a permutation group I	p. 155
On p-singular elements in Chevalley groups in characteristic p	p. 169
Experiments in coset enumeration	p. 183
A presentation for the Thompson sporadic simple group	p. 193
Computing automorphism groups of finite groups	p. 201
Regular orbits and the [kappa](GV)-problem	p. 209
The computational matrix group project	p. 229
Finding p'-elements in finite groups of Lie type	p. 249
Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture	p. 257
Deterministic algorithms for management of matrix groups	p. 265
Nearly simple matrix groups: desiderata and suggestions	p. 281
Cyclic matrices and the MEATAXE	p. 291
What do we know about the product replacement algorithm?	p. 301
On the complexity of the endomorphism problem for free groups	p. 349
Talks	p. 361
List of participants	p. 365
Table of Contents provided by Blackwell. All Rights Reserved.