Some Remarks on the Existence of Certain Unramified $p$-extensions

Nomura, Akito

doi:10.3836/tjm/1406552429

Cited by 4 publications

(5 citation statements)

References 8 publications

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“…With a little extra work, we can determine when a solution can be found with specific ramification. Some results of this nature in more specific instances were proven in [16] [17] [18] by Nomura and some general results can be found in [24]. Proof.…”

Section: The Unramified Brauer Embedding Problemmentioning

confidence: 88%

“…There are other results of a similar flavor to this one classifying unramified extensions of families of number fields. For instance, there are results for the ℓ-and ℓ 2torsion of the class group over cyclic degree ℓ fields [8] [9] [14] [15] [20] and some results for nonabelian p-extensions of quadratic fields or cyclic fields of prime degree q = p due to Nomura [16] [17] [18] [19]. Closest to the direction of this paper are results due to Lemmermeyer classifying unramified G-extensions of quadratic fields for G one of several small nonabelian 2-groups [11] [12], for example: Theorem 1.2.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this paper will be to generalize these results using class field theory and the theory of embedding problems. This approach follows the same basic idea as Nomura [16] [17] [18] [19], by using local conditions to say something about the solution to an embedding problem.…”

Section: Introductionmentioning

confidence: 99%

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Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations

Alberts¹

2017

Preprint

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We study solutions to the Brauer embedding problem with restricted ramification. Suppose G and A are a abelian groups, E is a central extension of G by A, and f : Gal(Q/Q) → G a continuous homomorphism. We determine conditions on the discriminant of f that are equivalent to the existence of an unramified lift f , i.e. a continuous homomorphism making the following diagram commute:As a consequence of this result, we use conditions on the discriminant of K for K/Q abelian to classify and count unramified nonabelian extensions L/K normal over Q where the (nontrivial) commutator subgroup of Gal(L/Q) is contained in its center. This generalizes a result due to Lemmermeyer, which states that a quadratic field Q( √ d) has an unramified extension normal over Q with Galois group H8 the quaternion group if and only if the discriminant factors d = d1d2d3 as a product of three coprime discriminants, at most one of which is negative, satisfying the following condition on Legendre symbols:for {i, j, k} = {1, 2, 3} and pi any prime dividing di.

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Section: The Unramified Brauer Embedding Problemmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations

Alberts¹

2017

Preprint

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“…This cell line comprises the most malignant adherent cells Grade IV, which should be cultured adhering to the bottom inner surface of the flask. [8][9][10][11][12][13][14][15][16] An example of a phase-contrast microscope image and a measured proliferation curve for YKG-1 glioblastoma cells are shown in Fig. 1.…”

Section: Preparation Of Brain Tumor Cellsmentioning

confidence: 99%

Development and estimation of brain tumor cells culture flask with acoustic window film for ultrasound exposure

Iwasiro

Watanabe

Yoshifumi³

et al. 2014

Jpn. J. Appl. Phys.

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Commercial polystyrene (PS) cell culture flasks were employed as containers of target brain tumor cells exposed to ultrasound. However, a problem was observed in that ultrasound energy was reflected at the surface of the flask with a different specific acoustic impedance from the water outside of the flask and the culture medium in the flask, and did not reach the cells sufficiently. Therefore, we prepared the original cell culture flask. This cell culture flask has thin polymer film acoustic windows for ultrasound irradiation at the top and bottom ends of a hollow cylindrical plastic pipe. We reached the conclusion that it is desirable to weld the poly(ethylene terephthalate) (PET) film or PS film as an acoustic window to the flask body by heat welding. The PS film acoustic window could be welded to the end of the PS or poly(menthyl methacrylate) (PMMA) flask body, but PET film acoustic window could not be welded to the end of the PS or PMMA flask body. The PET film acoustic window welded to the flask main body by ultrasound welding has sufficient durability to ultrasound sonication and excellent cellular adhesiveness.

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“…In [25] A.Numera has studied a similarly problem which noted by P (F, Γ), formulated as follows: P (F, Γ): For a given Galois extension F/Q and finite group Γ, does there exists a Galois extension M/F/Q satisfying the conditions:…”

Section: Introductionmentioning

confidence: 99%

On some metabelian 3-groups and applications I

Derhem¹,

Talbi²

2016

GJOM

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Let G be a 3-class group of maximal class, and γ2(G) = [G,G] its derived group. Assume that the commutator factor group G ∕ γ2(G) is of type (3,3) and the transfers Vχ2(G) → γ2(G) and VH→ γ2(G) are trivial, where χ2(G) is the biggest subgroup of G such that [χ2(G), γ2(G)] ⊆ γ4(G), and, H is one of its maximal normals subgroups different to χ2(G). Then G is completely determined with the isomorphism class groups of maximal class defined by B.Nebelung in [24]. Moreover the group G is realised. At the end numerical examples illustrating the results are given.

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Some Remarks on the Existence of Certain Unramified $p$-extensions

Cited by 4 publications

References 8 publications

Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations

Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations

Development and estimation of brain tumor cells culture flask with acoustic window film for ultrasound exposure

On some metabelian 3-groups and applications I

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