Inverse Galois TheoryInverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory. In all these areas important progress was made in the last few years. The aim of the book is to give a consistent and reasonably complete survey of these results, with the main emphasis on the rigidity method and its applications. Among others the monograph presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems combined with a collection of the existing Galois realizations. |
Contents
II | 1 |
III | 2 |
V | 3 |
VI | 7 |
VII | 9 |
X | 13 |
XII | 15 |
XIII | 18 |
CXIV | 186 |
CXVI | 189 |
CXVII | 191 |
CXVIII | 193 |
CXIX | 194 |
CXXI | 196 |
CXXII | 197 |
CXXIII | 199 |
XV | 21 |
XVI | 22 |
XVII | 25 |
XIX | 27 |
XX | 29 |
XXI | 30 |
XXII | 33 |
XXIV | 34 |
XXV | 36 |
XXVI | 39 |
XXVII | 41 |
XXVIII | 42 |
XXIX | 44 |
XXX | 46 |
XXXI | 48 |
XXXII | 49 |
XXXIII | 51 |
XXXIV | 52 |
XXXV | 53 |
XXXVI | 56 |
XXXVII | 59 |
XXXVIII | 61 |
XXXIX | 62 |
XL | 64 |
XLI | 65 |
XLII | 67 |
XLIII | 69 |
XLV | 71 |
XLVI | 74 |
XLVII | 78 |
XLVIII | 80 |
L | 81 |
LI | 85 |
LII | 87 |
LIII | 89 |
LIV | 90 |
LVI | 92 |
LVII | 95 |
LVIII | 97 |
LX | 98 |
LXI | 100 |
LXII | 101 |
LXIII | 104 |
LXV | 106 |
LXVI | 107 |
LXVII | 109 |
LXVIII | 113 |
LXIX | 114 |
LXX | 115 |
LXXI | 116 |
LXXII | 117 |
LXXIII | 120 |
LXXIV | 121 |
LXXV | 122 |
LXXVI | 123 |
LXXVII | 125 |
LXXVIII | 128 |
LXXIX | 133 |
LXXX | 134 |
LXXXI | 136 |
LXXXII | 137 |
LXXXIII | 138 |
LXXXIV | 140 |
LXXXV | 142 |
LXXXVI | 144 |
LXXXVIII | 146 |
LXXXIX | 148 |
XC | 149 |
XCI | 150 |
XCII | 153 |
XCIV | 154 |
XCV | 156 |
XCVI | 158 |
XCVII | 160 |
XCVIII | 161 |
XCIX | 162 |
C | 163 |
CI | 166 |
CII | 167 |
CIII | 170 |
CIV | 173 |
CV | 174 |
CVII | 175 |
CVIII | 177 |
CIX | 178 |
CXI | 180 |
CXII | 183 |
CXIII | 184 |
CXXIV | 201 |
CXXVI | 205 |
CXXVII | 207 |
CXXVIII | 209 |
CXXX | 211 |
CXXXI | 213 |
CXXXII | 215 |
CXXXIII | 217 |
CXXXV | 219 |
CXXXVI | 221 |
CXXXVII | 225 |
CXXXVIII | 227 |
CXL | 228 |
CXLI | 231 |
CXLII | 234 |
CXLIII | 236 |
CXLIV | 237 |
CXLVI | 239 |
CXLVII | 240 |
CXLVIII | 244 |
CXLIX | 246 |
CLI | 248 |
CLII | 253 |
CLIII | 255 |
CLIV | 257 |
CLV | 258 |
CLVI | 258 |
CLVII | 261 |
CLVIII | 263 |
CLIX | 266 |
CLX | 268 |
CLXI | 270 |
CLXIII | 271 |
CLXIV | 272 |
CLXV | 274 |
CLXVI | 276 |
CLXVIII | 278 |
CLXIX | 281 |
CLXX | 285 |
CLXXII | 286 |
CLXXIII | 287 |
CLXXIV | 289 |
CLXXV | 291 |
CLXXVI | 293 |
CLXXVII | 296 |
CLXXVIII | 299 |
CLXXIX | 303 |
CLXXX | 304 |
CLXXXII | 307 |
CLXXXIII | 309 |
CLXXXIV | 311 |
CLXXXV | 315 |
CLXXXVII | 317 |
CLXXXVIII | 319 |
CLXXXIX | 321 |
CXC | 323 |
CXCII | 327 |
CXCIII | 331 |
CXCIV | 332 |
CXCV | 334 |
CXCVII | 337 |
CXCVIII | 341 |
CXCIX | 342 |
CC | 347 |
CCII | 350 |
CCIII | 355 |
CCV | 359 |
CCVI | 360 |
CCVIII | 362 |
CCIX | 364 |
CCX | 366 |
CCXI | 370 |
CCXII | 371 |
CCXIII | 372 |
CCXIV | 374 |
CCXV | 375 |
CCXVI | 377 |
CCXVII | 379 |
CCXVIII | 381 |
CCXIX | 384 |
CCXXI | 386 |
CCXXII | 388 |
CCXXIII | 389 |
CCXXIV | 390 |
CCXXVI | 393 |
CCXXVII | 395 |
Other editions - View all
Common terms and phrases
algebraically closed assumption Aut(G automorphism braid orbit canonical epimorphism centralizer character characteristic conjugacy classes conjugate contains Corollary corresponding cyclic decomposition group defined degree denote elements of order epimorphism exists a geometric extension of constants factor group field extension field Ñ field of definition finite group fixed field fundamental group GA-realizations Gal(N/K Galois realizations geometric Galois extension group extension group G hence Hilbertian homomorphism Hurwitz braid group inertia group Inn(G involutions irreducible isomorphic kernel H Lemma Let G maximal subgroups moreover morphism normal subgroup number fields numerator divisor obtain orthogonal groups parametric permutation representation polynomial possess G-realizations prime divisors profinite proof of Theorem proper solution Proposition proves ramified rational function rational function field rationally rigid resp result Rigidity Theorem satisfies simple groups solution field solvable structure constant subfield symmetry group trivial unipotent unramified yields