Displaying similar documents to “Galois groups of tamely ramified p -extensions”

Asymptotics of number fields and the Cohen–Lenstra heuristics

Jürgen Klüners (2006)

Journal de Théorie des Nombres de Bordeaux

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We study the asymptotics conjecture of Malle for dihedral groups D ℓ of order 2 ℓ , where ℓ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen–Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

On Galois cohomology and realizability of 2-groups as Galois groups

Ivo Michailov (2011)

Open Mathematics

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In this paper we develop some new theoretical criteria for the realizability of p-groups as Galois groups over arbitrary fields. We provide necessary and sufficient conditions for the realizability of 14 of the 22 non-abelian 2-groups having a cyclic subgroup of index 4 that are not direct products of groups.

Capitulation for even K -groups in the cyclotomic ℤ p -extension.

Romain Validire (2009)

Journal de Théorie des Nombres de Bordeaux

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Let p be a prime number and F be a number field. Since Iwasawa’s works, the behaviour of the p -part of the ideal class group in the ℤ p -extensions of F has been well understood. Moreover, M. Grandet and J.-F. Jaulent gave a precise result about its abelian p -group structure. On the other hand, the ideal class group of a number field may be identified with the torsion part of the K 0 of its ring of integers. The even K -groups of rings of integers appear as higher...

Invariance groups of finite functions and orbit equivalence of permutation groups

Eszter K. Horváth, Géza Makay, Reinhard Pöschel, Tamás Waldhauser (2015)

Open Mathematics

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Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes...

Galois realizability of groups of order 64

Helen Grundman, Tara Smith (2010)

Open Mathematics

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This article examines the realizability of groups of order 64 as Galois groups over arbitrary fields. Specifically, we provide necessary and sufficient conditions for the realizability of 134 of the 200 noncyclic groups of order 64 that are not direct products of smaller groups.