Number fields unramified away from 2

John Jones

doi:10.1016/j.jnt.2010.02.005

Number fields unramified away from 2

John Jones

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Consider the set of number fields unramified away from 2, i.e., unramified outside {2,∞}. We show that there do not exist any such fields of degrees 9 through 15. As a consequence, the following simple groups are ruled out for being the Galois group of an extension which is unramified away from 2: Mathieu groups M11 and M12, PSL(3,3), and alternating groups A_j for 8<j<16 (values j≤8 were previously known).

Original language	English (US)
Pages (from-to)	1282-1291
Number of pages	10
Journal	Journal of Number Theory
Volume	130
Issue number	6
DOIs	https://doi.org/10.1016/j.jnt.2010.02.005
State	Published - Jun 2010

Keywords

Number field
Prescribed ramification

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2010.02.005

Cite this

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title = "Number fields unramified away from 2",

abstract = "Consider the set of number fields unramified away from 2, i.e., unramified outside {2,∞}. We show that there do not exist any such fields of degrees 9 through 15. As a consequence, the following simple groups are ruled out for being the Galois group of an extension which is unramified away from 2: Mathieu groups M11 and M12, PSL(3,3), and alternating groups Aj for 8",

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AB - Consider the set of number fields unramified away from 2, i.e., unramified outside {2,∞}. We show that there do not exist any such fields of degrees 9 through 15. As a consequence, the following simple groups are ruled out for being the Galois group of an extension which is unramified away from 2: Mathieu groups M11 and M12, PSL(3,3), and alternating groups Aj for 8

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KW - Prescribed ramification

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Number fields unramified away from 2

Abstract

Keywords

ASJC Scopus subject areas

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