The admissibility of A5

Gordon, Basil; Schacher, Murray

doi:10.1016/0022-314x(79)90029-5

Cited by 15 publications

(4 citation statements)

References 3 publications

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“…We give some references for the interested reader. For G = A 4 , A 5 see [24], [25], respectively. In fact, for these two groups stronger results hold.…”

Section: Examplesmentioning

confidence: 99%

Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions

Macedo,

Newton

2019

Preprint

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Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus R 1 K/k Gm. We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.

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“…We give some references for the interested reader. For G = A 4 , A 5 see [24], [25], respectively. In fact, for these two groups stronger results hold.…”

Section: Examplesmentioning

confidence: 99%

Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions

Macedo,

Newton

2019

Preprint

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“…This conjecture was studied extensively (e.g. [4], [5], [6], [10], [11], [21]) and proven by Sonn for solvable groups in a series of papers ( [3], [23] and [24]).…”

Section: Introductionmentioning

confidence: 99%

“…The first part of this question is known to have an affirmative answer for metacyclic G ([14, Theorem 27]) and for some small order groups: A 5 ( [11]), the central extension SL 2 (5) of A 5 ([9]), A 6 , A 7 ( [22]), the double covers of A 6 and A 7 ([8]), PSL 2 (7) ( [1]) and PSL 2 (11) ( [7]).…”

Section: Introductionmentioning

confidence: 99%

Tamely ramified subfields of division algebras

Neftin

2013

Journal of Algebra

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For any number field K, it is unknown which finite groups appear as Galois groups of extensions L/K such that L is a maximal subfield of a division algebra with center K (a K-division algebra). For K = Q, the answer is described by the long standing Q-admissibility conjecture.We extend a theorem of Neukirch on embedding problems with local constraints in order to determine for every number field K, what finite solvable groups G appear as Galois groups of tame maximal subfields of K-division algebras, generalizing Liedahl's theorem for metacyclic G and Sonn's solution of the Q-admissibility conjecture for solvable groups.

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“…For G = A 4 , S 4 , A 5 , S 5 , A 6 , A 7 , there exist Q-adequate Galois extensions L/Q with Gal(L/Q) ∼ = G. We give some references for the interested reader. For G = A 4 , A 5 see[25],[26], respectively. In fact, for these two groups stronger results hold.…”

mentioning

confidence: 99%

Explicit methods for the Hasse norm principle and applications toA_nandS_nextensions

Macedo¹,

Newton²

2021

Math. Proc. Camb. Phil. Soc.

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Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus \[R_{K/k}^1{\mathbb{G}_m}\] . We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.

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The admissibility of A5

Cited by 15 publications

References 3 publications

Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions

Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions

Tamely ramified subfields of division algebras

Explicit methods for the Hasse norm principle and applications toA_nandS_nextensions

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The admissibility of A5

Cited by 15 publications

References 3 publications

Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions

Explicit methods for the Hasse norm principle and applications to $A_n$ and $S_n$ extensions

Tamely ramified subfields of division algebras

Explicit methods for the Hasse norm principle and applications toAnandSnextensions

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Explicit methods for the Hasse norm principle and applications toA_nandS_nextensions