Intro
Contents
Preface
Notation and Conventions
CHAPTER I: GROUPS WITH COMMUTATOR RELATIONS
1. Nilpotent sets of roots
2. Reflection systems and root systems
3. Groups with commutator relations
4. Categories of groups with commutator relations
5. Weyl elements
CHAPTER II: GROUPS ASSOCIATED WITH JORDAN PAIRS
6. Introduction to Jordan pairs
7. The projective elementary group I
8. The projective elementary group II
9. Groups over Jordan pairs
CHAPTER III: STEINBERG GROUPS FOR PEIRCE GRADED JORDAN PAIRS
10. Peirce gradings

11. Groups defined by Peirce gradings
12. Weyl elements for idempotent Peirce gradings
13. Groups defined by sets of idempotents
CHAPTER IV: JORDAN GRAPHS
14. 3-graded root systems
15. Jordan graphs and 3-graded root systems
16. Local structure
17. Classification of arrows and vertices
18. Bases
19. Triangles
CHAPTER V: STEINBERG GROUPS FOR ROOT GRADED JORDAN PAIRS
20. Root gradings
21. Groups defined by root gradings
22. The Steinberg group of a root graded Jordan pair
23. Cogs
24. Weyl elements for idempotent root gradings

25. The monomial group
26. Centrality results
CHAPTER VI: CENTRAL CLOSEDNESS
27. Statement of the main result and outline of the proof
28. Invariant alternating maps
29. Vanishing of the binary symbols
30. Vanishing of the ternary symbols
31. Definition of the partial sections
32. Proof of the relations
Bibliography
Subject Index
Notation Index