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Generic polynomial
About: Generic polynomial is a research topic. Over the lifetime, 608 publications have been published within this topic receiving 6784 citations.
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TL;DR: In this article, the problem of identifying the set K (G, Ω ) of Galois number fields with given Galois group G and root discriminant less than the Serre constant Ω ≈ 44.7632 was studied.
19 citations
TL;DR: Using class field theory, this work gets bounds for the order of the 4-torsion on J"X(F"q), the group of points defined over F"q on the Jacobian of a hyperelliptic curve X/F" q.
19 citations
TL;DR: In this article, it was shown that the number of equivalence classes of regular embeddings of a group G into InHol (G ) is equal to twice the total number of fixed point free endomorphisms of G.
19 citations
TL;DR: In this paper, it was shown that the Galois group of the generic polynomial with degree d is the wreath power of the symmetric group with degree n. This result was partially completed by the late R.K. Odoni.
Abstract: In 1985, Odoni showed that in characteristic $0$ the Galois group of the $n$-th iterate of the generic polynomial with degree $d$ is as large as possible. That is, he showed that this Galois group is the $n$-th wreath power of the symmetric group $S_d$. We generalize this result to positive characteristic, as well as to the generic rational function. These results can be applied to prove certain density results in number theory, two of which are presented here. This work was partially completed by the late R.W.K. Odoni in an unpublished paper.
19 citations
TL;DR: In this paper, an explicit formula for the number of Galois extensions of a given local field with the prescribed Galois group U 4 (F p ) consisting of unipotent four by four matrices over F p.
19 citations