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Hughes D.R., Piper F.C. — Projective Planes
Hughes D.R., Piper F.C. — Projective Planes



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Название: Projective Planes

Авторы: Hughes D.R., Piper F.C.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 291

Добавлена в каталог: 10.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
(V, l)-desarguesian      108
(V, l)-transitivity      99 108
Absolute elements      48 234 239 244 247
Addition in a PTR      117
Affine geometry      63
Affine plane      63 82
Alternative division ring (alternative field)      139 154
Andre nearfield      190
Andre plane      191 207
Andre quasifield      187
Andre's Theorem      103
Annihilator      16
Artin — Zorn Theorem      139 149
Aut $\mathscr{P}$      33 90 253
Automorphism of a plane      21
Autotopism      173 175
Autotopism triangle      173
Axis of a perspectivity      38 95
Baer collineation      91
Baer subplane      82
Baer subset      81 92
Bruck — Kleinfeld Theorem      139 193
Bruck — Ryser Theorem      80 87
Cartesian group      130
Cayley table      116
Cayley — Dickson algebra      193
Central collineation      95
Centre of a division ring      152 170
Centre of a perspectivity      38 95
Centre of a skewfield      6
Characteristic of a connected set      259
Closed Baer subset      92
Closed configuration      77 219
Closure of a configuration      221
Collineation      21 90
Collineation group      90 253
Complete quadrilateral (Theorem of)      43
Complete sub-geometry      20
Configuration      105 219
Confined configuration      220
Confined core      220
Congruence partition      160
conic      50 243 250
Connected set      258
coordinates      26 110
Core of a configuration      220
Core of a group      11
Correlation      21 90 234
Cross ratio      41 54
Degenerate plane      77 219
Dense subset      81
Derivation      202
Derivation set      202
Derived plane      203
Desargues' configuration      105
Desarguesian plane      76 154
Design      246 285
Dickson commutative division ring      195 249
Difference set      262
Division ring (semifield)      134 154 170
Dual plane      14 22 78 134
Dual space      14 22
Dual translation plane      100 154
Duality (principle of)      78
Elation      95 258
Elation flag      258
ellipse      68
Equivalence of configurations      52
Extension of a configuration      222
Exterior line      242
Faithful permutation group      9 254
Fano plane      284
Field theory      5
Flag      220 257
Frame      24
Free closure      219 222
Free equivalence      227
Free extension      222
Frobenius group      12
Full collineation group      90
Full extension      222
Fundamental theorem of projective geometry      30
g-dimension      19
Galois field      7
General linear group      13
Generalised Andre plane      201
Generation      221
Grassman's identity      19
Group theory      9
Hall plane      187 209
Hall PTR      125
Hall quasifield      183 214
Hall's multiplier theorem      269
Harmonic conjugate      44
Hermitian polarity      48
Hjelmslev plane      285
Homogeneous coordinates      24
Homology      95 259
Homomorphism      21 232
Hughes plane      196 212
Hyperbola      68
Hyperplane      19
I.P. division ring      135 154
Incidence matrix      85
Incomplete sub-geometry      20
Inherited collineation      216
Interior line      242
Inversive plane      215 285
Involution      92
Irregular polarity      247
Isomorphism      21
Isotopism      176
Joachimstal's equation      50
Kernel of a congruence partition      162
Kernel of a quasifield      159
Knot of an oval      244
L.I.P. division ring      135
Latin square      121
Left nucleus      170
Lenz — Barlotti classification      109 284
Linear PTR      120 127
Linear transformation      13
Little projective group      40
Loop      116
Maximal closed configuration      93
Middle nucleus      170
Moufang plane      101 139 151 154
Multiplication in a PTR      117
Multiplier      269
Nearfield      134 154
Net      217
Norm      8 187
Normal form (for Latin squares)      122
Nucleus of a division ring      170
Nucleus of an oval      244
One-step extension      222
Open configuration      220
Open rank      220
Openly finite (o.f.) configuration      220
Orbit      10
Orbit theorem      257
Order of a projective plane      79
Order of an affine plane      84
Orthogonal group      53
Orthogonal latin square      121
Orthogonal polarity      48 247
Oval      241 250
Pappian plane      76 154
Pappus' configuration      26
Pappus' theorem      25
parabola      68
Parallel class      82
Parallelism      82
Parametric coordinates of a conic      52
Parametric coordinates of a line      33
Partial spread      217
Partition of a group      161
Pascal's theorem      56
Perspective      106
Perspectivity      38 95
Pickert's PTR      126
Planar collineation      91
Planar ternary ring      114
Polarity      21 45 91 234 239
Prime field      6
Primitive group      12
Principal isotope      178
Projective geometry      19
Projective line      20
Projective plane      20 77
Quadrangle      77
Quadratic form      48
Quadrilateral      77
Quasicentral collineation      91
Quasifield      131 154 157
Quasigroup      116
Quasiperspectivity      91
Quaternion      6
R.I.P. division ring      135
Regular permutation group      11
Regular polarity      247
Replaceable net      217
Right nucleus      170
Right quasifield      134
Secant line      242
Segre's Theorem      243 250
Self-polar triangle      49
Semi-linear transformation      13
Semi-nuclei      170
Semi-regular permutation group      11
Semifield (called division ring)      134 154 170
Shear      173
Singer group      71 262
Skewfield      5 139 154
Skornyakov — San Soucie Theorem      140
Socle      223
Special line (of affine plane)      85
Splitting field      7
SPREAD      166 217
Stabilizer      10
Stage of an element      223
Sub-geometry      20
Subplane      81 85
Tangent line      51 242
Ternary ring      113
Transitivity      10 99 108
Translation group      100 160
Translation line      100
Translation plane      100 154 157
Translation point      100
triangle      77
Unimodular group      40
Unital      57 246
Unitary group      62
Unitary polarity      48 247
Vector space      13
Wagner's Theorem      272 277
Weak quasifield      158
Wedderburn's Theorem      7
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