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Dickson L.E. — Linear Groups with an Exposition of Galois Field Theory
Dickson L.E. — Linear Groups with an Exposition of Galois Field Theory

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Название: Linear Groups with an Exposition of Galois Field Theory

Автор: Dickson L.E.

Аннотация:

Hailed as a milestone in the development of modern algebra, this classic exposition of the theory of groups was written by a distinguished mathematician who has made significant contributions to the field of abstract algebra. The text is well within the range of graduate students and of particular value in its attention to practical applications of group theory — applications that have given this formerly obscure area of investigation a central place in pure mathematics. These applications include the theory of the solvability of equations, theory of differential equations, complex number systems, and — preeminently — the foundations of geometry, where Euclidean or parabolic geometry, elliptic geometry, and hyperbolic geometry (corresponding to zero, positive, or negative curvature, respectively), can be completely characterized by groups. Linear Groups is divided into two parts. The first contains an extensive and thorough presentation of the theory of Galois Fields and is especially valuable for its enormous wealth of examples and theorems. The second part features a comprehensive discussion of linear groups in a Galois Field and contains a survey of the known simple groups of finite composite order. The author provides comprehensive detail about each group, much of which cannot easily be found elsewhere.


Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1901

Количество страниц: 203

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      89 110 115 117 151 179 200 201 299 309
Abstract field      9 13
Abstract group      287 289 292 300
Additive-field      5
Additive-group      49 269
Alternating group, 4 letters      269
Alternating group, 5 letters      279 290
Alternating group, 8 letters      259 290
Alternating group, k letters      289
Basis-system      49
Betti — Mathieu group      64 67 69
Canonical form      221 237 244
Characteristic determinant      80
Characteristic equation      222
Class of quantic      29
Class of residue      3 6 7
Commutative group      262 265
Commutative substitution      193 229
Compound of group      145
Configuration 27 lines      303
Congruent      3
conjugate      52 100 236
Cubic surface      303 306
Cyclic base      266
Dihedron group      265
Doubly-transitive      248 261
exercises      19 42 70 216
Existence of Galois F      14 19
Exponent of function      19
Exponent of mark      11
Factors of composition      81 91 94 191 192
Fermat's theorem      4 11
Field      5
First hypoabelian      201 208
First orthogonal      131 159 191 292 299 309
Four-group      267
Galois field      6 14
General linear homogeneous group      69 75 77 124 146 147 226 290
Group      65; see “alternating” “icosahedral” “dihedron” “tetrahedral” “octahedral” “symmetric” “linear” “general” “special” “simple”
Group $G_{168}$      303
Group $G_{20160}$      259
Group $G_{25920}$      293
Group $G_{51840}$      306
Hermite's theorem      59
Homogeneous      see “general” “special”
Hyperabelian group      115 183 209 298
Hyperelliptic      307
Hyperorthogonal group      131 264
Hypoabelian      see “first” “second”
Icosahedral      278 283 302
Index of subgroup      286 307
Infinity (mark)      260
Invariant of degree      2 126 218
Invariant, quadratic      144 153 156 191 194 197 206
Irreducible      10 15 44
Isomorphic      99 164 174 183 194 208 209 287 298 308
Linear fractional group      87 126 132 164 174 179 193 194 208 242 259 260 286 302 303
Linear independence      10 52
Mark      9
Modulus      3 6
Multiplier Galois F      51 270
Newton's identities      53
non-isomorphic      260 309
not-square      44 48
Octahedral group      269 282
Order of field      5 10
Orthogonal      see “first” “second”
Period of mark      11
Pfaffian      147 172
Primitive irreducible quantic      21 35 44
Primitive root      13 36
Quadratic equation      46; see “invariant”
Rank      49
Reduced quantic      63
Representation of substitutions      55
Residue      3 6
Second hypoabelian      201 209
Second orthogonal      159 191 194
Self-conjugate      82 117 279
Simple group      87 97 100 120 138 152 191 212 260 286 307 309
Special linear homogeneous group      82 125 147 151 153 300
squares      44 48
Substitution-quantic      55 63
Surface third order      303
Symmetric group, 6 letters      99
Symmetric group, k letters      287
Tetrahedral group      268 282
Transformation of indices      80
Transformed subst.      81 288
Transitive      248 261
Trieder      304
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