Section 2. Scheerer extensions of loops

Chapters in this book

1. Frontmatter I
2. Preface V
3. Notation VII
4. Contents IX
5. Introduction 1
6. Part I. General theory of transitive sections in groups and the geometry of loops
7. Section 1. Elements of the theory of loops and the relations with group theory 13
8. Section 2. Scheerer extensions of loops 42
9. Section 3. Nets associated with loops 53
10. Section 4. Local 3-nets 60
11. Section 5. Loop-sections covered by 1-parameter subgroups and geodesic loops 65
12. Section 6. Bol loops and symmetric spaces 80
13. Section 7. Bol nets 95
14. Section 8. Strongly topological and analytic Bol loops 100
15. Section 9. Core of a Bol loop and Bruck loops 102
16. Section 10. Bruck loops and symmetric quasigroups over groups 120
17. Section 11. Topological and differentiable Bruck loops 129
18. Section 12. Bruck loops in algebraic groups 143
19. Section 13. Core-related Bol loops 150
20. Section 14. Products and loops as sections in compact Lie groups 166
21. Section 15. Loops on symmetric spaces of groups 174
22. Section 16. Loops with compact translation groups and compact Bol loops 194
23. Section 17. Loops having a sharply transitive normal subgroup in their group generated by the left translations 208
24. Part II. Smooth loops on low dimensional manifolds
25. Section 18. Loops on 1-manifolds having a locally compact left translation group 235
26. Section 19. Topological loops on 2-dimensional manifolds 249
27. Section 20. Topological loops on tori 256
28. Section 21. Topological loops on the cylinder and on the plane 262
29. Section 22. The hyperbolic plane loop and its isotopism class 276
30. Section 23. Two-dimensional loops having a 3-dimensional solvable Lie group as their group generated by the left translations 289
31. Section 24. 2-dimensional Bol loops having a 4-dimensional Lie group as the group generated by their left translations 317
32. Section 25. Classification of differentiable 2-dimensional Bol loops 321
33. Section 26. Collineation groups of 4-dimensional Bol nets 329
34. Section 27. Strongly left alternative plane left A-loops 335
35. Section 28. 2-dimensional loops having a Lie group as the group generated by all translations 338
36. Section 29. Multiplicative loops of locally compact connected quasifields 344
37. Bibliography 351
38. Index 359