Minimal solvable nonic fields

Jones, John W.

doi:10.1112/s1461157013000077

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Mean-root Normalization and The Comparison Interval1

Comparing An Algebra With Its Splitting Field1

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2014

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“…Then the theorem just proved can be applied through its corollary |d 1−F (G)/n K gal /Q | ≤ |d K/Q | to obtain all K with |d K/Q | at most B = β 1−F (G)/n . This computation is carried out in [Jon12] for the primitive nonic groups 9T 9, 9T 14, 9T 15, 9T 16, 9T 23, and 9T 27 to obtain the corresponding nonic fields with smallest absolute discriminant. This particular application served as the catalyst for the present paper.…”

Section: Mean-root Normalization and The Comparison Intervalmentioning

confidence: 99%

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The tame-wild principle for discriminant relations for number fields

Jones

Roberts

2014

Algebra Number Theory

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Consider tuples of separable algebras over a common local or global number field, related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best possible divisibility relations among the discriminants. We show that for many resolvent constructions, these divisibility relations continue to hold even in the presence of wild ramification.Comment: 31 pages, 11 figures. Version 2 fixes a normalization error: |G| is corrected to n in Section 7.5. Version 3 fixes an off-by-one error in Section 6.

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Section: Mean-root Normalization and The Comparison Intervalmentioning

confidence: 99%

“…. This computation is carried out in [Jon12] for the primitive nonic groups 9T 9, 9T 14, 9T 15, 9T 16, 9T 23, and 9T 27 to obtain the corresponding nonic fields with smallest absolute discriminant. This particular application served as the catalyst for the present paper.…”

Section: Comparing An Algebra With Its Splitting Fieldmentioning

confidence: 99%