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book describes a constructive approach to the inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is isomorphic to G. Further, if there is such a Galois extension, find an explicit polynomial over K whose Galois group is the prescribed group G. The main theme of the book is(More)
Around 1830 Galois described a procedure for assigning a finite group G to a polynomial p(x) = x n + a 1 x n−1 + · · · + a n−1 x + a n , where a 1 ,. .. , a n are rational numbers. This group (which is now called the Galois group of p(x)) " measures " the difficulty in finding the roots of this polynomial; in particular, it tells us whether or not p(x) can(More)
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