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Hirschfield J.W. — Projective Geometries over Finite Fields
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Íàçâàíèå: Projective Geometries over Finite FieldsÀâòîð: Hirschfield J.W. Àííîòàöèÿ: This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1980Êîëè÷åñòâî ñòðàíèö: 488Äîáàâëåíà â êàòàëîã: 22.05.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Nucleus of a cubic curve 241 250—252 Nucleus of a quadric 114 Null polarity 34—36 Null polarity on a line 124 Null polarity, canonical form for a 111—112 Orbits of a projectivity 152—156 Order of a linear transformation 48—49 Order of a primal 49 Order of a projectivity 48—49 Order of a semi-linear group 420—421 Order of a variety 51 Ordinary polarity 34 36 Ordinary singularity 222 Oval 70 163—186 232—239 413—418 Oval, regular 174 182 209—211 Oval, translation 182—186 Ovaloid 70 Pappus's Theorem 159—161 Parabolic Quadric 106—111 114—115 Parallel class 38 Parallel lines 38 332—335 Pascal hexagon 394 Pascal line 394 397 Pencil 53 Pencil, full syzygetic 276 Pencil, syzygetic 271 Pentad, harmonic 407 Pentad, non-harmonic 407 Pentastigm 55 Pentastigm, diagonal points of a 139—140 Perfect difference set 78—79 96 Permutation group 244 Perspectivity 157—161 PG(2,11) 219 PG(2,13) 211—212 PG(2,16) 179 PG(2,2) 208 214 219 221 312—313 387—389 PG(2,3) 208 214 219 312—313 377—378 390—392 PG(2,4) 208 214 219 243 312—313 355 378—381 392—397 PG(2,5) 208 214 219 312—313 356 381 397—398 PG(2,7) 208—209 219 312—313 356—357 381—383 PG(2,8) 208—211 219 221 235 383—384 401—406 PG(2,9) 208 219 406—414 PG(3,2) 82—85 Plane 29 Plane curve 221—232 Plane curve, absolutely irreducible 221 Plane curve, component of a 221 Plane curve, degree of a 221 Plane curve, irreducible 221 Plane curve, order of a 221 Point 29 37 Point of a variety 49 Point of inflexion 222 Point, associated 128 132—133 Point, base 5 3 Point, complex 50 Point, external 165—166 170—171 201 Point, ideal 38 74 Point, imaginary 50 Point, internal 165—166 170—171 201 Point, model 225 Point, multiplicity of a 52 222 Point, proper 74 Point, real 50 225 Point, simple 52 222 Point, singular 52 222 Points, complex conjugate 50 polar 33 Polar line 245 Polar, conic 245 Polar, first 245—246 Polar, quadric 245 Polar, quadric, indeterminate 245 Polar, second 245—246 Polarity 32—37 110—115 Polarity in the plane 169—174 Polarity on a line 123 Polarity, Hermitian 35—36 110 147—148 Polarity, null 34—36 110—111 124 Polarity, ordinary 34 36 110 169—173 Polarity, pseudo 34 36 112—113 173—174 Polarity, symplectic 34 36 Polarity, unitary 34 36 Pole 33 Polygon 55 Polygram 55 Polynomial 2 174—186 Polynomial, characteristic 43 46—48 Polynomial, invariants of a 14—27 Polynomial, minimum 43 Polynomial, permutation 2 174—186 Polynomial, primitive 6 83 Polynomial, subprimitive 6—7 46—48 74—76 Polystigm 55 Primal 49 Primal, absolutely irreducible 50 Primal, component of a 50 Primal, degree of a 50 Primal, irreducible 50 Primal, order of a 50 Primal, regular component of a 50 Prime 29 Prime coordinates 32—33 Primitive element 1 6—8 Primitive element, polynomial 6 S3 Primitive element, root 1 6—8 Principle of duality 31 Projective group 40 124—128 149—157 244 419—424 Projective group, space 29 Projective group, space, axioms for 38—39 Projective group, special linear group 41 419—424 Projective group, triad 377 Projective group, triangle 376 Projectivity 30 Projectivity between two lines 157—161 Projectivity in the plane 149—157 Projectivity on a line 119 124—128 Projectivity, canonical form for a 40—46 124—128 149—157 Projectivity, cross-axis of a 161 Projectivity, cyclic 74—96 155 Projectivity, extended symbol of a 45—46 Projectivity, orbits of a 152—156 Projectivity, order of a 48—49 Projectivity, standard 152 Projectivity, symbol of a 45—46 Pseudo polarity 34 36 Pseudo polarity in the plane 173—174 Pseudo polarity on a line 124 Pseudo polarity, canonical form for a 112—113 Quadrangle 55 Quadrangle, complete 55 Quadratic equations 3 13 Quadric 97—115 Quadric on a line 122 Quadric, canonical form for a 98—102 104—107 Quadric, character of a 107 110 Quadric, condition for singularity of a plane 144—146 Quadric, degenerate 97 Quadric, elliptic 106—111 114—115 Quadric, group of a 110 Quadric, hyperbolic 106—111 114—115 Quadric, nucleus of a 114 Quadric, number of points on a 108—110 Quadric, parabolic 106—111 114—115 Quadric, plane 140—141 144—146 Quadric, projective index of a 107 Quadrilateral 55 Quadrilateral, complete 55 Quartic equations 13 16—18 22—27 Quasi-conical set 190—196 Quintuple, negative 134—135 Quintuple, positive 134—135 Rank of a k-arc 201 205—206 Rank of a point 204 Real index of a point 222 Real point 50 225 Real tangent 222 Reciprocity 33 Reducible variety 51 Regular component 50 Regular oval 174 182 209—211 Representing vector 29 Resultant 10 S-invariant 3—11 s-line 393 Secant 70 Second polar 245—246 Secundum 29 Segre's Theorem 165—169 Self-conjugate point 33 Self-conjugate prime 33 Self-polar triangle 171—174 Series, complete 54 Series, linear 54 Similarity of matrices 43 Simple point 52 222 Simplex of reference 32 Singular cubic curve 254—268 Singular plane quadric 140—141 144—146 Singular point 52 222 Solid 29 Space, tangent 52 span 70 Special linear group 41 419—424 Spinode 223 SPREAD 70 72—74 83 Spread, k-fold 81 Standard projectivity 152 Sub-Hermitian curve 148—149 229 Subexponent 6—7 Subgeometry 85—96 Subprimitive polynomial 6—7 46—48 74—76 Subprimitive root 6—9 91—92 subspace 29 52—53 Subspaces, characterization of 67—69 Subspaces, number of 65—67 Subspaces, sets of 69—74 Superharmonic tetrad 121 129 133—135 surface 49 51 Symbol of a linear transformation 45—46 Symbol of a projectivity 45—46 Symmetric fc-arc 207 Symplectic group 419—424 Symplectic Polarity 34 36 t-design 37 Tactical configuration 37 Tactical configuration, 160—161 Tactical configuration, 160—161 Tactical configuration, 242—243 Tangent line to a curve 222 Tangent line to a k-set 70 Tangent line to a variety 52 Tangent line, prime 110 114 Tangent line, space 52 Tangential coordinates 32—33 Tetragram 55 Tetrastigm 55 Tetrastigm, diagonal points of a 138 Translation Oval 182—186 triangle 55 Triangle, inflexional 271 276 Triangle, self-polar 171—174 Trisecant 70 Uniform k-arc 212—214 Unisecant 70 Unisecant of a k-arc 163 166—168 Unit point 32 Unit prime 32 Unitary group 419—424 Unitary group, polarity 35—36 Variety 49 62 Variety, absolutely irreducible 51 Variety, component of a 51 Variety, degree of a 51 Variety, dimension of a 51 Variety, Hermitian 97—115 Variety, irreducible 51—53 Variety, order of a 51 Variety, point of a 49 Variety, quadric 97—115 Variety, reducible 51 Vector space 29 Vertex 54
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