P-polynomials and H-Galois extensions
نویسندگان
چکیده
منابع مشابه
PRESENTING GALOIS GROUPS OF INFINITE TAMELY RAMIFIED p-EXTENSIONS
Let p be a rational prime and S a finite set of rational primes. We are interested in the structure of GS(p), the Galois group of the maximal p-extension of Q unramified outside S (and ∞ if p = 2). In the case that p ∈ S, many GS(p) are known explicitly [12], but in the case that p ∈ S, very little is known. Throughout this report we shall assume that p ∈ S. The author developed methods to comp...
متن کاملGalois groups of tamely ramified p - extensions par Nigel BOSTON
Very little is known regarding the Galois group of the maximal p-extension unramified outside a finite set of primes S of a number field in the case that the primes above p are not in S. We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.
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For any number field F (not necessary of finite degree) and prime number p, let Lp(F ) denote the maximal unramified p-extension over F , and put G̃F (p) = Gal(Lp(F )/F ). Though the structure of G̃F (p) has been one of the most fascinating theme of number theory, our knowledge on it is not enough even at present: It had been a cerebrated open problem for a long time whether G̃F (p) can be infinit...
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Given an integer n and a group G we estimate the probability that a random, monic, degree n, p-adic polynomial has Galois group isomorphic to G. A comparison is made with classic results concerning Galois groups of random, monic, degree n polynomials with integer coefficients. We conclude by analyzing the probability that a random, monic, degree n polynomial in Z[x] has these properties: its Ga...
متن کاملExtensions of Galois Connections
Galois connections play a very important role in the theory of continuous lattices and their various generalizations. (See, for example, [1], [2], [a], [4], [5], [7] and [9].) Morphisms of continuous lattices, as defined in [2], are precisely those upper adjoints of Galois connections which preserve directed sups. In [1] Bandelf and Ernd suggested that the right choice of morphisms for Z-contin...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90039-1