| 41. | These permutations together form a permutation group, also called the Galois group of the polynomial ( over the rational numbers ).
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| 42. | It is known that a Galois group modulo a prime is isomorphic to a subgroup of the Galois group over the rationals.
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| 43. | It is known that a Galois group modulo a prime is isomorphic to a subgroup of the Galois group over the rationals.
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| 44. | If the Galois group is supersolvable or more generally monomial then all representations are of this form so the Artin conjecture holds.
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| 45. | One resolvent can tell if the Galois group of a polynomial is a ( not necessarily proper ) subgroup of given group.
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| 46. | Igor Shafarevich proved that every solvable finite group is the Galois group of some extension of "'Q " '.
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| 47. | Sheaves endowed with nontrivial endomorphisms, such as the action of an algebraic torus or a Galois group, are of particular interest.
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| 48. | ;"'Frobenius field "': A pseudo algebraically closed field whose absolute Galois group has the embedding property.
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| 49. | Then the question is this : is there a Galois extension field such that the Galois group of the extension is isomorphic to?
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| 50. | After that, one applies Hilbert's irreducibility theorem to specialise, in such a way as to preserve the Galois group.
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