|
Chapter I:
Quasigroups and loops |
|
I.0 |
Introduction |
1 |
I.1 |
Groupoids, quasigroups and loops |
2 |
I.2 |
Subgroups and subloops |
8 |
I.3 |
Nuclei and center of a quasigroup |
16 |
I.4 |
Inverse property |
20 |
I.5 |
Multiplication group and inner mapping group |
24 |
I.6 |
Isomorphy |
26 |
I.7 |
Homomorphy theory for quasigroups |
28 |
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|
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Chapter II: Quasigroups and geometry |
|
II.1 |
Quasigroups and 3-webs |
34 |
II.2 |
Isotopy, parastrophy, isostrophy |
39 |
II.3 |
Web configuations and loop laws |
47 |
II.4 |
Affine incidence planes |
52 |
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Chapter III: Isotopy theory for quasigroups |
|
III.1 |
Isotopy for groupoids |
57 |
III.2 |
Isotopy theory for quasigroups and loops |
59 |
III.3 |
Autotopisms |
66 |
III.4 |
Pseudo-automorphisms of quasigroups |
74 |
III.5 |
Derivatives |
79 |
III.6 |
The isotopy-isomorphy property of loops |
82 |
|
|
|
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Chapter IV: Moufang loops |
|
IV.1 |
Basic properties of Moufang loops |
88 |
IV.2 |
Moufang's theorem |
93 |
IV.3 |
Some theorems concerning pseudo-automorphisms, the nucleus, the Moufang center
and self-adjoint subgroups of Moufang loops |
97 |
IV.4 |
Isotopy
of Moufang loops |
101 |
IV.5 |
Commutative Moufang loops |
107 |
IV.6 |
Bol loops
| 112 |
|
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Chapter V: Some classes of quasigroups |
|
V.1 |
Totally symmetric quasigroups
| 122 |
V.2 |
Distributive and entropic quasigroups |
131 |
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Bibliography |
143 |
|
Subject index |
146 |