What do we know about the product replacement algorithm?

Chapters in this book

1. Frontmatter I
2. Preface V
3. Table of contents VII
4. Probabilistic recognition of orthogonal and symplectic groups 1
5. Janko’s simple groups J2 and J3 are irreducible subgroups of SL85(5) with equal centralizers of an involution 21
6. Recognizing simplicity of black-box groups and the frequency of p-singular elements in affine groups 39
7. Improved algorithms for the Tits alternative 63
8. A constructive recognition algorithm for the matrix group Ω (d, q) 79
9. On constructive recognition of a black box PSL( d , q ) 95
10. Fast recognition of classical groups over large fields 113
11. Parallel GAP: Mature interactive parallel computing 123
12. Computing with infinite polycyclic groups 139
13. Computing the maximal subgroups of a permutation group I 155
14. On p-singular elements in Chevalley groups in characteristic ρ 169
15. Experiments in coset enumeration 183
16. A presentation for the Thompson sporadic simple group 193
17. Computing automorphism groups of finite groups 201
18. Regular orbits and the k(GV)-problem 209
19. The computational matrix group project 229
20. Finding pʹ-elements in finite groups of Lie type 249
21. Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture 257
22. Deterministic algorithms for management of matrix groups 265
23. Nearly simple matrix groups: desiderata and suggestions 281
24. Cyclic matrices and the MEATAXE 291
25. What do we know about the product replacement algorithm? 301
26. On the complexity of the endomorphism problem for free groups 349
27. Talks 361
28. List of participants 365